Do they require phone number?
Swim got bitfinex and polo account both anonymous.
Recently because I use the same phone number at bittrex Swim end up having to tell them my passport and stuff.
That sucks.
Oneday bittrex may notify my government that Swim have Bitcoins. Swim is screwed.
Swim wants to create another bittrex account anonymously.
Do they require phone number?
If you have been reading about that is going on with Bitfinex and other major sites, phone number will be the least of information you have to provide which will even be verified before anything can be done.
Swim wants to create another bittrex account anonymously.
The crypto market has gone beyond this point and the site you are focusing on are the ones who can do without you and they are big enough to get the attention of regulatory authority which force them to do the right thing.
Even if you manage to get a new phone number will you also get a new passport and ID? Mind you in verifying your account they don't only cross check the phone number with their database but also every details you are providing for that effect. If you then register and you have to verify before withdrawal, it then means you either comply or forfeit your funds with this condition that you have accepted in their Terms and Conditions.
Your fear of releasing your details to the government is valid because all that will be needed is the right court judgement and warrant then you are good to face whatever the government is bring against you.