As Scott says, unless you have the situation where one user is recording BPs for another user (great idea BTW !) then just use Creator.
Creator will automatically link to the User that was logged on at the time the thing was created. (but see below).
Then you can just do BP Readin’s Creator’s UserName … to show the name.
There seems to be some confusion over “User” and “User Name” in your set up. The User’s name is field on user, so having a field called User Name set to User seems a little odd. It isn’t the user’s name, it is the WHOLE thing from tthe user table.
The issue with using Creator is that it doesn’t work very well in the Data view, as it requires you to be logged on. You would need to create the page in the app and set up the logon for it to work.
The set up you have, with User Name, would work in Data View, you have set up “User Name” to search on email address as a field (thats the “Primary Display Field” box, so start typing an email address and you will get a list of users, select on and it will allocate it to the BP reading.