Another way to say "list of/with names" would be "names list" or "name list" or "names' list"? The last one I suppose is not correct, because possesive is used for persons, am I right?
Name list and names list are both valid. Which one is better might depend on the context.
Names' list is incorrect, but for a different reason.
It's incorrect because when you use the possessive apostrophe s, it suggests that the list belongs to the names, or that the list is intended to be used by the names, which doesn't make any sense. It's not important that names are not persons. Even with a set of people, we would not use this phrase. Or if we did, it would have a different meaning.
For example, a presidents' list would not be a list of presidents, it would be a list (of something else) that was made for presidents.
Note: I see a lot of English language learners making comments about the possessive apostrophe s only being correct in reference to people. This is incorrect; there is no such rule. I don't know why teachers are telling their students this. All kinds of inanimate objects can "possess" things: the sun's rays, the ocean's bounty, the food's smell, the paint's luster, the table's finish, the car's make, and on and on and on.
Using "name" as an attributive noun is acceptable "a name list" or even hyphenated "name-list". Similarly we can get "fruitbowl" (this compound has become so common that it is increasingly written as one word) and "stupid-word-dictionary".
However "list of names" is a normal and natural way of describing this:
Have you got the list of names for the party? I want to check if Kathy has been invited.
In particular contexts it may be given a special name. In school, a list of names is a "register", or sometimes a "roll" (from which we get the expression "roll call"; at one time the list of names would have been written on a roll of paper).