I have many names, but one. I have infinite names, but none. All, but none, are mine. What am I?

I have many names, but one.

I have infinite names, but none.

All, but none, are mine.

Hint:

Think about it from a figurative POV.

• Is this related to computer languages in any way? Jul 10, 2016 at 21:03

It's a bit of a weak solution and maybe silly, but it's the only thing that came to my mind at the moment.

I think you are..

something.

I have many names, but one.

If something refers to the presence of a thing, then something can be anything except for nothing, since by our earlier assumption nothing would refer to the absence of a thing.
So something can be anything except nothing.

I have infinite names, but none.

Since anything is a list of infinite possibilities of things, and something can be anything, there's an infinite list of possibilities of what something can be. However since it must be something, it cannot be nothing.
So something can have any name, except for nothing, the only thing it cannot be.

All, but none, are mine.

Just repeating the earlier "conclusions". Something can be anything except nothing.

• I hope this is it. Good job making none and one the same. Jul 11, 2016 at 14:00

Are you:

Arya Stark?

Many names, but one -

A girl has no name

Infinite names, but none -

the many faced God has many faces

All but none, are mine -

She is not the person she imitates

• Since the hint was think figuratively not literally I doubt this is the answer, but damn does it fit! Jul 11, 2016 at 5:25

You are:

All numbers except Zero

I have many names, but one.

You have the names of all the numbers except Zero, which is one name

I have infinite names, but none.

There are infinite numbers, hence infinite names and None stands for Zero, which isn't included.

All, but none, are mine.

All numbers except Zero, which is none, belong