I discovered I was doing this too

Usually I had tracked their thought and was responding before they finished saying it, rather than starting another topic altogether, but it's just as hard to break the habit even knowing.. I usually manage to wait for them to finish, but sometimes it's quite an effort, like part of me is tapping fingernails on the table to make them hurry up and say what I know they've already said somehow.. don't think it's psychic but my brain just leaps that way.
On names however, it doesn't leap or follow or vaguely grasp in passing, I'm hopeless, can listen carefully, repeat it back to them, and a few minutes later, nothing remains
I can often recall an entire conversation with someone, complete with their animal's details, bizarre odd salient facts, when and where we were, and still have no clue what the name is! As a former professional listener it was a useful skill set but I only had one person at a time, for an hour, with written notes to read before and writeup after, so it was way easier

And remembering an odd fact or sentence from months before at the right moment was often a major bonus to therapeutic work, more so than the name I reckon, so I wouldn't complain but now.. memory is just not my strong point at all!
PS, techniques include a mantra of "wait" whenever I feel my mouth ready to engage.. Sometimes it feels like making a dog sit with a biscuit on its nose, but at least it makes me smile while I'm waiting