This is a common misconception about PCSOs. They aren't meant to be Police Officers, nor "half" police or anything like that. They do a completely different job, yet because they wear a reflective jacket people think they're trying to be Police.
PCSOs are there to "be there" for the community, and to gather intelligence. They don't have police powers because they are NOT law enforcement. Think of them more like school crossing guards or "ask me for help" people at an airport, except they're there for police-related business. More like assistants in a shop than the security guard.
We can't afford to have a copper on every street corner, and that would be a complete waste of money. The regular officers have to go around to response jobs, and then it means public areas just aren't patrolled anymore. PCSOs are a good halfway, but NOT a replacement or pretend police officer.
PCSOs actually have the same powers of arrest as any other citizen. However, only some areas allow them to use this and arrest people until a Police Officer arrives. Some areas allow them to carry handcuffs too, but they are there "just in case" rather than it being their job to apprehend criminals.
Personally, I think they should look less like police officers and be more identifiable as their own community role. Because people think of them as "pretend police" they have no respect for them and don't understand the job they do. Which is a good and useful job that we need someone to do.
(In related news, I'm a police officer)
Anyone can ask you for your name and address, you don't have to give it to them. You always have the right to remain silent should you choose, you don't have to be told it to use it.
If the police want to report you for an offence (to go to court), they need to know your address so that they can send you the summons. If you refuse to tell them your address, or if it's fake, they can arrest you and make sure you are taken to court.
If this was a PCSO, they do have the power to 'require' you to provide your name and address for some offences. They can detain you for up to 30 minutes if you don't, until a Police Officer can come and arrest you.
If it was some other council officer or warden, some of them have limited powers. If you're unsure, ask them. If you feel you're being treated unfairly or detained illegally, ask the police to attend.