Is there a last number and then numbers without names?

Answer 1

All numbers have names. None of them can not have names.

Observe, a proof...

Suppose x is the smallest number that doesnt have a name.

Then, "the smallest number that doesnt have a name" is in itself a name.

So, x has a name.

Proof by contradiction... x is not the smallest number that doesnt have a name.

But since x is defined to be the smallest, we can deduce that there is no smallest number that doesnt have a name.... because if there was, it would be x, and it would lead to a contradiction.