Group messages splitting

I have a group text with two other people— one iPhone and one Android. Recently the group text between us split so that now there are two threads, one that gives just their names, and one that has their names PLUS my name. The problem is that sometimes their messages come on one of the threads, sometimes the other. I will ask a question on one thread, and they will answer on the other.

I tried to delete one of the threads, but under edit the only option is “delete and block this group”. Doing that blocked the other thread as well. I reinstated the first, tried again with the second. Same result. I rebooted between each step.

Both of my friends deleted the thread on their phones and started new threads. If either of the threads are blocked on my phones, I get nothing.

Theirs are threading perfectly.

Is there a way to delete a group text and NOT block? Is there another fix?