>Not everyone is great at self-selling, and people who move up in the company are the ones who hype their personal brand, not necessarily those who are the best at their roles. I don't know how to solve this as it's a personality issue

You need a strong manager or leader willing and able to reign individuals in. This person needs to open the discussion space to others and prevent the loudest (and it sure seems often like the most opinionated) from interrupting.