Follow-up "Real-time validation for user's name and username"

This is a follow-up issue for https://gitlab.com/gitlab-org/gitlab-ce/issues/56787

We added real-time validation for the username on the register page in https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/25017

We should add this to the user profile page as well by leveraging the same pattern introduced in https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/25017