I think that there are three possibilities here
1) That someone of a similar name but different address has been charged and convicted, but for some reason the conviction has been noted against you.
2) That someone of a similar name was reported for the offence, but the charge was made against you: for some reason you didn't become aware of this, and you were convicted in your absence
3) That actually you were fare-dodging, and you were caught, and you have been lying to us. If that's the case, there's nothing we can do to help. But on the basis of what you have told us, I think this is staggeringly unlikely so I apologise for putting this point so baldly, and I won't consider it further.
What you should do about the first two possibilities starts off the same, but then diverges. To start with, you need to contact the court to find out quite what has happened. It looks as if you have started in on this - but you should aim to do this quite quickly, because if (my option (2)) you were wrongly convicted then you have only 21 days to formally let the court know by making a 'statutory declaration' that you didn't know about the prosecution. What a 'statutory declaration' does is to set the conviction aside, and it will be relisted and heard again - but in practice what we see here is that if the wrong person was prosecuted, then the railway withdraw their prosecution and you can walk away with a clean record. If (option (1)) it's just that the records are a bit muddled then hopefully getting in touch will be enough for the court to put their records right.
So get in touch with the court. Given the current Covid-19 position there is probably a lot to be said for emailing them (
TV-BerkshireMCEnq@Justice.gov.uk seems to be the address for both Reading and East Berkshire (i.e. Slough) magistrates' courts). If you don't get a response by the time the 21 days are running a bit short, you might want to phone (0118 980 1800, 10.00 am - 2.00 pm) or maybe send a letter with proof of posting from a post office to make sure that you get your argument in.