You give the information you are required to give under law - your name and address. And make sure you give your real name and address as giving false information is a further offence. An RPI, ticket inspector etc can ask for additional information but you do not have to supply it. Whilst the TOC may view that as you being un co-operative, they will not be able to use your disinclination to give additional information against you in court, although as others have said the TOC may see it as a reason not to settle out of court And to continue with a prosecution, although I have not seen any proof of that.
It is highly unlikely that I will ever be in this situation as I always buy the correct ticket but if I was faced with this, I certainly wouldn’t be giving out bank details, NI numbers etc and yes I can remember both my NI and Driving licence numbers!
I remember watching an episode of The Tube on the tellybox a few years ago when a TFL RPI Or whoever asked someone he had stopped for not having a ticket to turn out his pockets, something that the RPI has absolutely no power to do and should never have asked.
If stopped give the information you are required to under law, give it truthfully and give nothing else in my book. Easy for me to say mind, I’ve never been stopped for having the wrong or no ticket. Nor will I ever be stopped for this as I always buy the correct ticket.
But to be blunt, if you buy the right ticket you‘ll have nothing to worry about.
I hate fare dodgers.