I set up groups for message with unique names. Now I cannot find them

Hi TomADAMS01,

Welcome to the Apple Community

You might find this other discussion on a similar topic useful :-)

https://discussions.apple.com/thread/253489818

Or, for more:

Browse this article:

Send and receive text messages on iPhone

Eg: Says: (Scroll to end of "Send a Messsage")

To view conversation details, tap the name or phone number at the top of the screen.

You can tap the contact to edit the contact card, share your location, view attachments, leave a group conversation, and more.

Complete article: https://support.apple.com/en-au/guide/iphone/iph82fb73ba3/ios

All the best :-)