It appears the OP mentions on another forum on Reddit, that their mother was home with them that day. Additionally it appears the name the TOC has is spelled rather differently than the OPs name, not just say a letter out.
A lot of speculation on what evidence the TOC has and a lot of focus on the OP having to find social media or Google timeline evidence of being elsewhere (on both threads). The OP hasnt even got to the plea hearing yet, and has to decide whether to plead guilty or not. A trial if any would be at a later date. If the OP hadnt committed the offence, they shouldnt really be pleading guilty but the choice is theirs.
I hope the OP gets some good legal advice. This type of case is not the first of its kind. People have given other peoples details before, and there have been threads on that.
The prosecution will have to be put to proof if this even gets to trial (they might even withdraw in the face of a not guilty plea... I know more speculation).
A good lawyer or prepared litigant in person would seek disclosure at plea hearing or before a trial, and would question the strength of the prosecution evidence either in a defence case statement or at trial or both. I am not a lawyer, but I recall a barrister writing once, the defence don't need to prove a negative, they need to shake enough doubt at the prosecution case.
Some things that stick out about the strength of the prosecution case, based on what has been written are as follows.
Who gives their correct address (so they can be contacted and prosecuted), but mispells their own name?
Faced with someone who only gave a name and address did the RPI request to see a bank card or anything on them with their name on it?
Did the TOC attempt to trace the purchase of the ticket presented by the "stoppee" to identify the likely holder. If they havent yet, (particularly if the OP has denied being the "stoppee" in correspondence) , why dont they instead of jumping to prosecution.
Does the TOC have any cctv or photgraphs of the person on the day when stopped or at any of the stations? The lack of (regardless of reasons why discussed above) does not harm the defence, it shows the prosecution doesn't have something that could connect the defendant to the "stoppee" particularly if the "stoppee" gave nothing else but a name and address.