Might be worth a survey of native speakers/residents of each respective country how appropriate their name database is and hwo important/appreciated fixing it would be.
Well, from my point of view, maintaining the name database is an ongoing process. We are in a lucky position, since our database is very good (we don't have unrealistic/fake names at all, we have of course highly uncommon names, but that I consider a richness). This means there is very little work needed, mostly checking for some uncommon names every now and then. However, any sort of "name your player freely" or "let's include the names managers give when applying into the database" feature would result in quality drop of our name database. That would really be a slap in the face for those of us who have worked on the database.
So, no harm in a survey, but the tools are already there. They are unfortunately very slow to use, but as an LA you anyway have the power to start the work on the current database as soon as you want. If a completely new database is needed, the best way would be to work on that offline with a group of dedicated people and then ask for the BB's to consider adding it/replacing the old one. We have almost 9000 first names and more than 20000 last names in our database, so the task is many cases is huge.
I wouldn't mind a name-your-player feature where you choose the name from the BB names database. As a one-off thing (like for winning a competition), there can be more freedom - but please do not mess with the databases, not the good ones anyway.