However, for the benefit of anyone who stumbles onto this thread when they have a similar problem, it may be worth pointing out that inaccuracies in name, address, date of birth and so on aren't of themselves a reason that will make the railway drop a challenge.
To work a couple of examples: let's say that you're Mr John Smith of 1 The Street, Anytown
EXAMPLE 1: You never use the train on Mondays, but you get a letter from the railway saying that you were caught fare dodging on Monday 7 August 2023. The letter is addressed to you, with your proper name and address. As it can't have been you (you never use the train on Mondays) you're within your rights to ignore the letter altogether as it's obviously someone else using your details, but as people have said earlier in this thread, it will probably save you hassle further down the road if you write back and explain that it's not you, and someone must have used your details to try and get away with it.
EXAMPLE 2: while you still don't use the train on Mondays, you do use it on Tuesdays, and on Tuesday 8 August you were caught fare dodging by a ticket inspector. You gave your details, but when you get a letter about being caught, it's addressed to Ms J Smuth at 11 The Street, Anytown. You can't say that the letter isn't for you in that you know that actually you were caught fare dodging: what the railway (and the law courts) are interested in is getting to the right person - whatever name and address is used to do so. You're going to have to deal with the railway accusing you of being a fare dodger as if you ignore it they will eventually turn up with the ticket inspector who as an eye witness will be able to identify you even if they haven't got your name and address quite right.