Fullname vs username and how to ask for username after Social Login

I am building a mobile application where users can post/rate songs they like.

I have three ways of registering: email+password, facebook login and google login.

From my personal experience, some people prefer apps that show full names of users as they seem more trustworthy and tend to avoid apps that show only usernames because it is believed that their content is not trusted; e.g "demonXX175 rated a song" (this may not seem trustworthy for users).

So I decided, that I will show full names (e.g John Doe) when a user posts content. That's why in the registration process, if a user signs up with email+password I ask for him to give his full name (with proper validations that it is a valid full name string, although this can be bypassed e.g John D instead of John Doe). Of course, if a user signs up with facebook/google then their full name is acquired automatically for them and the majority of cases it will be their correct full name. Also if he signs with facebook, then I also get his profile picture, and this is also shown to his app profile (on the other hand a silhouette profile pic is shown, that they can change later).

But, I think that when a user registers with email/password, and I implicitly demand from him to give me his full name, is a little bit aggressive as a user may not want to give full name. Also there may be problems like many users have a full name that is more or less the same (as full names are not unique)

My question is what would you do in a situation like that? Would you show full names or usernames for users? Also if you show usernames, then that means that when a user connects with facebook/google then you should ask for them to give a unique username, after they successfuly connected with fb/google, and that may be overhead of the registration process.