Password:
Paracanthurushepatus (Paracanthurus hepatus)
Overall question details:
The professor is Dr. Linnaeus better known as Carl Linnaeus who is known for his creation of Index Cards (likely not important for this puzzle) and his creation of the Linnaeus Taxonomy. Based on the fact that the white board says "My Family" and most of the images are of animals, I believe taxonomy (more specifically the families) are important for this puzzle
Images (listed in order shown on the board (number refers number shown on the picture)):
9:
Cetomimidae a.k.a Flabby whalefish, family = Cetomimi[d]ae
2 (listed in order from top left to bottom right (across then down)):
2.1:
Columbo(character)/Peter Falk(actor)
2.2:
Hercule Poirot(character)/Sir Peter Ustinov(actor)
2.3:
Inspector Clouseau(character)/Peter Sellers(character)
2.4:
Trunk a.k.a. an elephant nose
Which together might mean:
All actors named Peter then an elephant nose => Peters' Elephantnose Fish, family = M[o]rmyridae
4:
Queen Parrotfish, family = Sca[r]idae
11:
Crocodile Icefish, family = Channichth[y]idae
1:
Pearlside, family = [S]ternoptychidae
OP's intended fish: Round Whitefish, family = [S]almonidae
5:
Zebra stripes and map is of Turkey, so a Zebra Turkeyfish family = Scor[p]aenidae
8:
Goatfish fish that can change their color (maybe to white and blue), family = Mullida[e]
OP's specific goatfish: Bicolor Goatfish (same family)
3:
This is an Upside-down Catfish ignoring the Asian upside-down catfish, they all share the same family = Mo[c]hokidae
10:
This is an image of Maurice Tillet known as the french angel => French Angelfish family = Pomacanth[i]dae
7:
Black Dogfish, family = Etmopt[e]ridae
OP's intended fish: Broadbanded Lanternshark (a.k.a dogfish), same family
6:
Southern Sandfish which lives off the coast of Australia/New Zealand (hence the kangaroo), family = Lepto[s]copidae
Pattern:
All of the clues are types of fish
Next Step:
Take the letter at the specified number of each fish's family in order shown on the blackboard and you get DORYSPECIES. Dory from Finding Nemo is a royal blue tang which the species name is Paracanthurus hepatus, which contains 20 characters
Footnote: @Neon612 helped find a bunch of the clues