You could try using a language transformer, which can be helpful in brainstorming. I used GPT-J at TextSynth, which gave me The Death Crew and The Worldview Warriors within the first few tries. I cannot say whether these are taken, but if you try enough, you should be able to get something novel. Another popular model is GPT-3 (sign-in required), which is more powerful. The key to successful use of language transformers is in prompt-crafting. Generally, the more context you provide (up to the memory limit), the better the result. An example prompt:
Welcome to the Mongol Rally of existential, philosophical wonder, where purpose is both found and lost. Many thought-provoking teams will be finding their presence here, but will any achieve permanence? Making a fierce entry with its red Suzuki Alto, a new Nietzsche-inspired team from Missing Valley, the
Note how the prompt ends in pregnancy. This allows the language transformer to take over from exactly that point in the sentence. While not always necessary, this approach can often get the desired result more up-front. Also, remember to check what it gives you is not already taken or otherwise coming from a copyrighted source. Searching the Web is probably a wise idea before officially using something it gives you. The examples I gave may well be in use out there, so be careful.