Head Coach question

[CaRef5]

Got a hypothetical for ya:

Team A begins with (guy 1) as the head coach. Halfway through the game his "assistant" begins to complain. The officials try to address the issue only to be told the "assistant" was the actual head coach.

The crew on the game says he can't do that because he began the game as the HC so he must finish it as the HC.

where can I find the rule that supports that or if there is one? (both NCAA and NFHS)

tried doing a search on this forum but no luck.

thanks!