I taught this concept to my children as "give before you take." I had occasion to remind my 32-year old about it yesterday when discussing how she would ask the school bus driver her name.
If you just say to someone "what is your name?" it can be alarming. Perhaps you want to know their name to complain about them. Perhaps you're one of those kids in schools who makes mean nicknames out of people's names. An alarmed person may avoid answering.
If you first give the person the piece of information you are asking for, it's reassuring. Whatever power a name has, you have volunteered yours. That makes people feel safer giving theirs. (This isn't logical, the bully could still make a mean nickname from your name, they were never planning to stay anonymous, but this is just an emotional reaction many people have.) It's even better if you start with a compliment. "I like your sweater! I'm HeavenlyHarmony, what's your name?" Or as I suggested to my daughter, "[granddaughter] enjoyed riding the bus with you yesterday. My name is [name], what's yours?"
Of course, I can't speak for your speech coach. I do find this concept (give a piece of information before bluntly demanding something from someone) really enables friendly and useful conversations. For example, if you just ask a friend "What are you doing this weekend?" they will likely give vague answers or try not to answer. You might be looking for help moving, or a dog sitter, or something else they fear they can't decline if they say they have nothing planned. If you say "I was thinking of going [whatever] this weekend, would you like to come?" they can accept, or tell you they have other plans. This is more pleasant for you both. Yet many people start conversations with blunt questions that leave others slightly alarmed. I wouldn't be surprised if your coach was working on this idea with you.