You could say a player's number is his trademark

The New York Times (free registration required) has an interesting story on the price athelets are willing to pay their teammates for a number. For instance:

When a prominent athlete joins a new team after contract talks, the negotiations in a high-stakes numbers game have often only just begun. Jeff Feagles, the punter for the Giants, wore No. 10 until he sold it to the rookie quarterback Eli Manning last spring for a one-week vacation in Florida. Then Feagles switched to No. 17, which he sold this off-season to receiver Plaxico Burress for a new outdoor kitchen at his home in Phoenix.

For some players a number is their brand.

For many professional athletes, a jersey number is a personal brand. It is worn on shoes and helmets, wristbands and turtlenecks. It inspires tattoos and is engraved on medallions the size of manhole covers.