I ported over to a new Android recently and most of my stuff migrated fine. I wasn’t getting my contact names on Google Hangouts, though—just the numbers were showing.
Solution: I went to settings > apps > Hangouts > Storage > and cleared Data and Cache. When I restarted Hangouts, it asked me if I wanted to allow Hangouts to access my contacts. I clicked next and confirmed. After that, my contact names started showing.