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There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

 

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors In the 100 blue eyes problem - why is the oracle necessary? (suggested by Bobson)

There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors In the 100 blue eyes problem - why is the oracle necessary? (suggested by Bobson)

There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors In the 100 blue eyes problem - why is the oracle necessary? (suggested by Bobson)

There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors In the 100 blue eyes problem - why is the oracle necessary? (suggested by Bobson)

There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors

There is no special name for such type of puzzles as far as i know.
But usually they are formulated in terms of hats worn by logicians.

If you google you can find a lot of puzzles of this type, for example, this:

The Logical Hats Puzzle. Logicians A, B and C each wear a hat with a positive integer on it such that the number on one hat is the sum of the numbers on the other two. They can see the numbers on the other two hats but not their own. They are given this information and asked in turn if they can identify their number. In the first round A, B and C each in turn say they don't know. In the second round A is first to go and states his number is 50. What numbers are on B and C?

Or this:

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats (as in diagram). The jailer explains that there are two red and two blue hats; that each prisoner is wearing one of the hats; and that each of the prisoners is only to see the hats in front of them but not on themselves or behind. The fourth man behind the screen can't see or be seen by any other prisoner. No communication between the prisoners is allowed.

If any prisoner can figure out and say to the jailer what color hat he has on his head all four prisoners go free. If any prisoner suggests an incorrect answer, all four prisoners are executed. The puzzle is to find how the prisoners can escape, regardless of how the jailer distributes the hats.

Also there was a lot of them on this site:

Guessing hat colors
Hats and Aliens
N logicians wearing hats of N colors In the 100 blue eyes problem - why is the oracle necessary? (suggested by Bobson)