Gym uniforms are a new custom cosmetic in the Galar region's Gym Challenge. In Galar, taking on the gyms has become a national spectacle with sportsmanship and showmanship being taken to a whole new level. All contestants are required to wear the standardized challenger uniform, with a custom jersey number, during their televised stadium battles.
The big twist to the Galar Gym Challenge is that challengers are more or less competing against each other in a semi-finals showdown to be the one to take on the Champion. With such a heightened sense of competition, it is only natural that challengers dress the part and sport a jersey number for their fans to represent.
Given the restrictions in attire, it comes as no surprise that trainers must also commit to a jersey number quite early on in Pokémon Sword and Shield. Applicants of the Galar Gym Challenge are asked to select a jersey number to be displayed on the uniform upon registration at the Motostoke stadium. The number must be one to three digits long and will appear on all uniforms acquired throughout the game, not just the challenger uniform.
Trainers should ensure the number is one hundred percent satisfactory before submitting it during registration, as the game will have to be restarted entirely in order to make any changes. Being the first main series title on console grants Sword and Shield the unique ability to make additions and tweak the game through patch notes. However, changing minor details such as jersey numbers is not likely a high priority for developers. Maybe when and if the ability to compete wearing various uniforms becomes available, Game Freak will take the opportunity to incorporate a number change option as well.
Only time will tell how Game Freak chooses to utilize patch updates. Currently, however, Gym numbers are chosen early on and stick with the trainer through the entirety of the game. Trainers will want to make sure they're satisfied with the number unless they're willing to restart the game entirely.