Well, that wouldn't be honest, and I don't see that I can advise you to be anything but honest.
I won't go into why honesty is the best policy - that's something that most of us learn in our early years and for those of us who don't universities have philosophy departments to discuss the issue. But just looking at things practically, it's by no means impossible that at some point you might want a job where it's important that you are honest. There are more jobs like that than you might think - obviously there are roles where you have charge of other people's money (working in a bank for example) but there are also jobs where you have other people's personal information (being a nurse or a doctor perhaps, or working in a council office or in recruitment), and there are also jobs where you are looking after other people's property (anything in a shop, a job where you drive the company's vehicle and so could make off with the car/van/lorry, a job in an office or factory where not everything is nailed down and you might steal the chair or the lathe or whatever). In all of these jobs the employer will want to know if you're honest - if you can be trusted with the information or assets that you have access to.
At first glance, you might think that being able to deny a fare-dodging conviction would be a good thing - it's not your name, so how can they link it to you? But it's surprising how things do get out. It might be that the court would eventually catch up with you (I think you've given your brother's address - what's to stop someone coming round and asking him if he knows of someone who might have given that address, or them looking into people who might have used that address falsely, and deciding that you are the person they're after?) or you might have a conversation in a tea break at work ('years back I got away with fare dodging as I gave a false name') that gets back to your boss. However it happens, I will make a prediction - if you're doing a job where you need to be seen to be honest, and your employer finds out that you didn't tell them about a conviction, then you will be sacked for gross misconduct. You won't be sacked because of the fare-dodging - most employers understand that people do silly things from time to time, and as long as you don't make a habit of it they won't mind. But you will be sacked because of not telling them: if you can't be trusted to admit to something minor like fare-dodging, then what else are you hiding from them? You even actively decided to hide your dishonesty by giving a false name, so what might you do with what your employer has trusted you with? You will have proved yourself not to be trustworthy, and that would mean that the employer couldn't trust you to do the job.
And there's one other thing. The fact that you've looked for advice here says to me that you're not happy that you will get away with using your false name. I don't know you, but if you are like everyone that I have ever met, you will feel a lot better about things if you tell the truth about your name. Even if you do get away with lying about it for the moment, there will always be the worry that someone will find out, and you will be caught. If you are honest about it as soon as possible, then whatever consequences there are will happen to you sooner rather than later: they will be dealt with, and over. You'll find it easier to sleep at night.