I have the exact same experience. In normal conversation, I'm usually pretty fine, but my stutter pops up whenever I plan out what I want to say (which includes saying my own name, because there's no word substitute for your own name...). It leads to me doing the same 10-second long "uh uh uh uh uh uh" thing you described. It's a bit of a relief to hear someone else in the same situation! I think it's a combination of the "vicious cycle" of stuttering (stutter leads to anxiety about stuttering, which leads to actually stuttering, which leads to more anxiety, etc) + the fact that we can't word substitute if we have specific lines to say + something else beyond our control maybe? It's definitely not the anxiety alone, because I sometimes stutter when I'm not anxious and I sometimes get anxious but end up maintaining fluency. Here's something that I've found helps me avoid stuttering: I take in a breath right before I begin speaking, exhale, and as soon as I hit the bottom of my exhale, I take in a breath and begin speaking. It's a weird timing trick that seems to help me trick my brain into not stuttering. Idk if I can really call it fluency, but it works. Anybody else ever try something like that?