Can cctv find out my name and address on a train?

Yeah I'd be surprised if BTP entertained that at all, you did after all have a valid ticket for travel?

Yes I did! It was valid and then because she thought I made a habit of buying them when I’m on the train (which I don’t) she made me go through my Trainline history which showed I’m a frequent traveller and always buy my ticket! Just really shakes me up these things because they make such a scene of you!

It sounds like they're just being an **** tbh. I'd be minded to make a complaint as threatening to have a paying customer taken away by police is a bit excessive and obviously affects how safe you feel travelling with them.

I know they prefer people to buy before they board, but it's just not always possible, but if THEY are willing to sell you a ticket on the train, surely you can also buy a valid ticket from another vendor?

That's not what the rules say.

Essentially, you are required to have a ticket with you at the point where you board the train if there are working facilities at that station to buy a ticket. OP had already broken the law before the point where they bought the ticket.

It does get confusing because in some cases a train guard can and will sell a ticket to you even if you could have bought a ticket at the station that you boarded at. But they should only do that if they know that you couldn't have bought a ticket at that station. (In areas where a penalty fare scheme is in operation, it's only certain people who are allowed to issue penalty fares; so if the person checking tickets isn't allowed to give penalty fares, then they'll probably just sell a ticket. If they can issue penalty fares, then they might choose to issue a penalty fare rather than sell a ticket.)

When a guard/inspector sees that you've bought a ticket while you're on the train, the suspicion is always going to be that you've only bought the ticket because you know/suspect that you're going to have to produce it. Perhaps at that point you've been on the train for some time, but you only buy a ticket from the most recent station that the train called at. That's probably why they checked your Trainline history.

The problem with making a complaint is that if OP tells the railway company what happened, then they're effectively admitting that they've committed an offence by boarding a train without being in possession of a valid ticket. In reality, I suspect it's very unlikely that they railway company will take any action, but it's not impossible.