User Profile image keeps changing in MacOS

It rather depends on who these users are.

If, for example, they are family members, then by all means let each have their own Apple Id.

You can set up family sharing, so for example apps purchased with one account are shared by all. Plus each gets 5GB of free storage.

Is the picture changing to the last selected picture, among those logins sharing the same Apple Account?

The user picture is taken from the icloud account. Since all mac accounts share the same icloud, you won't be able to assign them different pictures.