When I start to type in the name of a recipient in the Message app possible recipients do not populate. For example, when I would have a recipient with the name 'Smith', I would only have to start with the letters 'S-M' until the rest of the name would populate. With 13.1 it no longers does that.
I have never had this problem with any previous Beta version of iOS 13.
I filed a bug report in the Feedback app.