I can relate to this too.
Some of the guys in my friend group are BAD for not letting others get words in. They really enjoy hearing the sounds of their own voices I think, but they’re still good people.
It really depends on the situation I think, and what ideas are in their head when they’re interrupting you. They could be just trying to contribute something more as they have gotten very excited from your story and want others (and you) to know immediately that they can relate, something like an “OMG this happened to me too, so the other day…”. (at which point you fold your hands and patiently wait for them to expel their vocal wind, and try not to get into any barreling wars with each other trying to get a word in). Or it could be something else (like a bully who just doesn’t value your opinion or respect you, so they make their own voices heard).
One thing that I’ve found, especially with some of my friends (speaking from my own experiences here), is you have to be able to hold your own ground when telling a story. If you’re passionate about what you’re saying, don’t let anyone deter you from telling it! If you see a couple of people put their heads down to look at their phones mid-story, or start up another conversation with the person beside them even while you’re still talking, than what I do is focus my story on the people who are actually paying attention and actively listening to the story. This will help you engage in your story more and make you feel better about telling it anyway. Because of this, you will appear more confident and have more fun telling the story anyway.
Usually what happens here from a social dynamics standpoint, is that you will attract more people in towards you and your story because they want to be a part of whatever “looks so fun” where you are. My favourite is when the people who ignored you actually turn back around and say “K wait, tell that again” when they see everyone else enjoying what you’ve said. To which I say something like “oh no that’s ok, you’d get bored with it” (giggle amongst yourself) or if you know them well enough, say “nah, you weren’t in it, so I figured you wouldn’t want to hear it”. Mad respect points among those listening right there and then start looking at your phone when they try to tell a story (haha totally kidding, ok I’m rambling here).
Now with my friends, you can play games like, when they look back up from their phones after the stories done, I say “Oh hi, welcome back”. Or if they interrupt me after I’ve started telling a story, I’ll say something like “Oh I didn’t know this was a duet” with an exciting smile on my face. That one usually gets laughs and quiets some mouths long enough for you to tell your story
Now some of these suggestions I wouldn’t recommend with someone you’ve just met of course, but sometimes people just need a little reminder to show some manners and that there are other people in the world besides themselves In any new situation, use the body language they teach you here at the SOP, show some confidence, and if someone interrupts you anyway (which some people will no matter what you do), just respectfully wait until they’re finished, agree with them and say “So as I was saying”, and carry on. (Don’t sound condescending when you do this, be honest).
Hope that helped a bit. I made myself laugh a couple of times writing this