The possessive is required here.

Changement de ses propres mots de passe.

Note that ses is both the possessive adjective for the third person pronoun (il/elle) and the indefinite pronoun on.

If you intend to say in the same sentence that the admin could change both his own and others’ passwords then the first proposal is incorrect. The first proposal only mean that the admin change his own passwords, not those of others.

Your second sentence is ambiguous in that “propre” would be understood as “proper” and not “own”.

So I would suggest you to write simply

Changement des mots de passe

But if you really want to remind that these passwords are personnal (aren’t they anyway?)

Changement des mots de passe personnels