According to Roger Sherman, under college football rules, “[i]t’s legal to change a player’s uniform number mid-season—all that matters is the roster submitted to the officials on gameday.” This ensures that the opposing team has the opportunity to review the changes. If the change was not noted before the game, “it would have had to be reported to the official and announced” when the player in question takes the field. There are additional rules, such as those governing changing a player’s number to the number of a player at a different position. Conversely, the NFL avoids any issues by prohibiting in-season number changes. [Source: Roger Sherman (12/30/24)] In an earlier article, Mr. Sherman explained that a college football player change jersey numbers in the middle of a game in order to be eligible to catch a forward pass (players must be wearing a number outside of the 50-79 range to be eligible to catch passes). Here, the NFL has a more sensible approach, allowing the Coach to declare an otherwise ineligible receiver eligible before a play. [Source: Roger Sherman (9/27/24), text fragment link]
Things I learned aside, I highly recommend reading the first source article. Mr. Sherman tells a very fun story about selling a fake punt with subterfuge in an otherwise sleepy bowl game between Bowling Green and Arkansas.