Seeing as most forms of travel and accommodations these days at some point require handing over an ID, I'm not sure you have a lot of options for
anonymity.
If you book a flight in a false or even just misspelled name, you may be refused boarding. Same with hotels, although they may be more amenable to making changes in person. But it's at their discretion.
To avoid that headache, you'd still have to book and provide your own name, and then it doesn't matter much if you paid in
crypto or fiat.
Think of booking travel with crypto just as a convenient way to pay if you already have crypto and don't want to exchange to fiat. It probably costs more than cashing out crypto at market rate and using fiat to pay, but that's the price of convenience.