There is no requirement to tell the police who you have booked your holiday with. Looking at my last notification earlier this year you need to tell them the flight number, carrier and accommodation address in section 1.
Unless you are using a TUI branded flight or hotel then they won't know you are on a TUI holiday.
Section 2 does ask for a booking number and agent but this information is voluntary and you do not have to provide it.
Although it maybe just easier to book a flight and hotel yourself rather than through a tour operator. You can often get the same selection of hotels and flights at a cheaper price.
Personally I am more worried about ETIAS next year as this may block travel to the EU