The magic system in a story I'm writing lets you learn magic abilities faster if you're bonded with someone. The people of that world tie a lot of culture and emotions to their magic and the bonds they formed to get them.
The main character bonds with people who are oppressed because of their magic type, and wants it to be known who gave him that ability, both so his enemies know they are hurting real people, and so if he dies they know who he died for.
Others seek to master one ability, and form teams with others who know the same ability so they can collectively perfect it. They form their identities around their shared ability, taking great honor in them and going on quests together.
Another reason people say their ability is because most people travel in groups in this world so they can grow their bonds and be stronger together. Saying their abilities helps their friends or followers learn the move even faster, and again its usually said in pride. Some people like saying the names of their abilities out of respect to whoever gave it to them or to show they are part of a specific school of magic.
There is one character that takes advantage of everyone's acceptance of being honest about their abilities and outright lies about what her abilities are lol. Another character is excited for everyone to know what he can do, even if they're an enemy. Most characters never say what their ability specifically does, but usually, the name of their ability carries some weight for them and helps grow their bonds, and they wish to honor it.