There are three broad types of "suicide hotline". Each behaves quite differently.
Firstly, there are lines associated with a health service, often called "crisis lines". The point of calling these lines is to get intensive help. They will assess your needs. They might decide that you need an ambulance. They might book you in for emergency clinical care. They will ask for information like your name, address, date of birth, and perhaps a little bit of medical history.
Secondly, there are "suicide prevention" lines run by charities. These are not directly connected to medical services and are more or less anonymous, with the usual "unless we think there is a threat to life" type of disclaimers. You don't have to share any information with them and there's nothing they can do if you don't. I found calling one of these to be utterly pointless. I hung up after the responder said "have you tried listening to podcasts?"
Finally, there are "listening" lines, also run by charities. Samaritans is one such example. These are not there to stop you from killing yourself, and they will not give advice of any kind. They will only call emergency services in limit circumstances, and will only do it during a call in very limited circumstances: if you ask them to, or if you pass out during the call. I've never felt pressured to give information, although sometimes late in a call I will give my first name. If you want in-depth discussion about suicide, truly free from judgement, a line like this is probably your best option.
Before calling a line, check their confidentiality policy.