If you create a custom login, you can do it (you’ll have to use query the members collection by id, get the corresponded email and then use user.login() to log the user in based on the retrieved email and filed out password. See:
https://www.wix.com/corvid/reference/wix-users/login
(if it’s secured enough for you)
You should think how you make sure all the user names are unique.