I was told I need to pay a penalty fare, my money is on my Oyster card so didn't really have any extra expenditure.
I'm not sure exactly what you mean by "didn't really have any extra" but this was your best opportunity to correct the problem if you possibly could do. Its' unfortunate that you didn't (or couldn't) take that opportunity.
If you
really could not pay, then the Inspector acted quite correctly and reasonably in asking you for your name and address, so that payment of the Penalty can be obtained later.
I gave my abbreviated name, and was asked whether this was my full name, I said no and gave my full name. The guard has now accused me of giving a fake name. How is that possible when I was not told what exact details needed to be given. When asked for my full name I gave it.
It's also unfortunate that you didn't seem to cooperate as helpfully as you could. I don't know what you meant by giving an abbreviated name, but because it didn't correspond when checked, it would have appeared to be a false name. That will be what the Inspector has now written in his report.
Do you think this is fair? It was not intentional.
Yes, it is fair to offer a simple Penalty fare when passengers hadn't paid the correct amount and to take their correct name and address so that the fare can be collected later. I do feel that the Company will think it is intentional that you didn't pay when asked and that not giving the most accurate name is intentional.
Perhaps your incident will be passed to an Investigator who will agree that the name you gave was not a deceitful attempt to avoid payment and will simply ask for the correct Penalty Fare plus some payment towards the Company's administrative costs.
But, if they suspect that you had tried to avoid giving your correct name and address, then, as
bb21 says, they have a clause in the Regulation of Railways Act specifically designed to capture people who give false details. It has been a common crime on the Railways for a great many years and prosecutions are regularly brought against passengers who do this.
. . . to be honest am I expected to just give my full details to a man who just asks for my details.
But he wasn't just "a man asking for your details", was he? He was a Railway Ticket Inspector - inspecting tickets on the Railways.
I think a criminal conviction and ruining my future is unbearable. Would you suggest I need a solicitor?
Not yet. Wait to see what the Company decides. I've already suggested that the investigator might agree that your name was adequate, and they'll just want the payment that you didn't make to the Inspector. But if not, then they'll write to tell you that they intend to prosecute you for giving a false name and address. At that point, a local law firm which specialises in Criminal Defence work should be able to assist, though I'm sorry to say that they'll be unlikely to make that crime go away.