Question: Is there a name for this?
Yes; generally it's just called fidgeting. People do it for different reasons; maybe they're bored, maybe they have high energy and they're restless being still, etc.
Is there a training to improve the ability to focus 100% on the communication?
For whom? I assume you mean the child, but are you focusing 100% on the communication, or are you focusing on the fidgeting he's doing?
It's not my intention to bring you up short. I'm only hoping to point out that interactions are a two-way street between different people. It's easy to be distracted by things your son is doing, and it's easy to interpret this as him not giving you his full attention, but you don't know what's going on in his head.
You can't force your son to keep his hands still, or to be more descriptive than he wants to be. You can ask for these things, but before you do, please consider what effect this will have. It important that your son knows how he answers is less important than what he says/thinks, and that how you feel when he answers is not more important than how he feels. So, maybe asking only when something is really important to you is better than trying to bring this behavior under better control the majority of the time.
I know people who don't like making eye contact even during superficial conversations. My job isn't to change them, it's my job to manage my end of the conversation. Of course, if it were my child, I would want the best for them, and would want them to learn to be comfortable making more eye contact. So I would encourage eye-contact, because I equate it with more successful social interactions.
It turns out that one of my adult kids is like that. And I did try to get him to make more eye-contact. And I was wrong. He is a very successful kid in every respect (and this isn't just the mother in me speaking.) Even with his less-than-my-ideal amount of eye contact.
But yes, there probably are a lot of things you can do to get him to be more attentive during conversations. But he has to be motivated to change. That's a lot harder to figure out, as is who benefits the most from trying to change a good kid's behavior.
I understand this difficulty you're having, trust me. I really do, and I sympathize.
When he's talking about things he's very interested in, does he talk more and fidget less?