iMessage splitting out conversations with one contact into multiple chains and changing the contact name

My iPhone has been creating multiple iMessage threads with some of my contacts for a few months and I haven't been able to figure out how to reconcile the different threads. Beyond that, it's now changed the contact name on one of the threads to the person's email address instead of their name. I thought I would try the "Add to Existing Contact' option, but that doesn't show up as a possibility under the "Info" screen. I'd like to figure out how to re-reconcile all of the iMessage chains together under the single contact name in a single thread. Any ideas of how to do that?