Ask your DM.
Everything in Tasha’s Cauldron of Everything is optional material to add to your game. It is up to your DM to allow or not to allow sidekicks at all, and so it is going to be entirely up to the DM to allow one of their unique NPCs to become a sidekick for the players. The rules printed in the Creating a Sidekick section have no restriction on “named” NPCs:
A sidekick can be any type of creature with a stat block in the Monster Manual or another D&D book, but the challenge rating in its stat block must be 1/2 or lower.
To join the adventurers, the sidekick must be the friend of at least one of them. This friendship might be connected to a character’s backstory or to events that have transpired in play. For example, a sidekick could be a childhood friend or pet, or it might be a creature the adventurers saved. As DM, you determine whether there is sufficient trust established for the creature to join the group.
So the rules even say it is up to the DM.