The register does not lie. When an artist stage name is registered in someone else name, that person controls how it is used commercially, regardless of who made it famous.
This happens constantly in the music industry. A label, a manager or a former partner files the mark during the early years, when nobody is thinking about paperwork. Years later, when the name is worth money, the artist discovers that the merchandising, the licensing and sometimes the ability to tour under that name sit with a third party.
How it happens
Mexico grants trademark rights to the first to file, not the first to use. Fame does not create a registration. If nobody in the artist camp files, someone else can, and the artist is left arguing bad faith under article 173 of the Federal Law for the Protection of Industrial Property, a remedy that requires evidence, time and money.
What to do instead
Three practical steps. First, file the stage name in your own name, or in a company you control, in the classes that matter: entertainment services, recordings, clothing, and any product line you might launch. Second, if a label or manager insists on holding the mark, negotiate an assignment on termination in writing. Third, review the register once a year to catch anyone filing something confusingly similar.
The cost of filing is a rounding error next to the cost of losing the name you spent a decade building.