Is there a way for a user to have an alias?

Users are means of authentication and authorization. This should not be confused in any way with whatever information is displayed on the front end.

By default wordpress core is guilty of not understanding the distinction, but in some contexts like comments it should be easy to add a “name” field to the comment form for logged in users, and use it for display. Other contexts like author archives will be hard to adjust to handling multiple “handles” for users and the easiest path would be to simply create an additional user.

Adjusting functionality of plugins most likely will be a matter of hit and miss, most likely mostly miss.

Tl;Dr;

Just create a second user, maybe install one of the user switchers plugins for easy switching when needed.