Is it possible to book an hotel being a minor?

Typically this is explicitly disallowed. However, in the U.S. one is typically only required to present a credit card (but no photo ID) in order to check in. If you have a credit card in your name, and as long as you don't look super-young, you might have no problems at all.

If you want to pay cash -- it probably won't work.

If you have a credit card, it's worth trying.

Or you could stay at a hotel where you never have to interact with a human in order to check in, such as Yotel NYC.

Both of my children have had issues renting hotel rooms in Canada - the US has similar rules - while under 21. Twice my youngest was stranded far from home with a credit card and the hotel had a policy forbidding him to rent a room. One place called us, and with our consent allowed it, the other (further away) did not but let him and his friends hang out in the lobby for 3 hours while his father drove there to get him. I redeemed an award stay for my oldest and made special arrangements in advance that it would be ok even though she was a few days shy of 21, and they still attempted to turn her away, but when I called the manager it was allowed. Both kids had credit cards in their own names.

This is worth checking out in advance. Call or email hotels and try to get it settled and booked in advance.