No, GTA 6 does not require an ID to play. Rockstar has not announced any identity verification, account linking with government documents, or age-check system beyond the standard platform age gates that already exist on PlayStation and Xbox.
What you do need is a PSN or Xbox Live account to buy and download the game, since there is no physical disc. Those accounts require you to enter a birth date, but that is not an ID check. On PlayStation, if you are under 18, a parent or guardian must manage the account, and the same basic rules apply on Xbox.
One practical note: the game is rated M for Mature by the ESRB, so stores and platform holders may ask for ID when you buy a gift card or use a payment method, but that is a retail policy, not a Rockstar requirement. Nothing in the official store listings or Rockstar Newswire mentions any ID or verification step to launch the game itself.