I studied an art based course and I had to disclose. I got on the course and finished (with a first), but I wished I'd changed my name beforehand. This was only due to someone finding out near the end.
The lead tutors knew about
the offence - although there were a certain amount of mitigating circumstances which they understood affected how I was at the time. They are still supportive and I got a very good reference from the head tutor.
Changing your name is a matter of hours/days by statutory declaration (depending on getting an appointment with a solicitor). It's then getting all the other things updated that has taken time. So perhaps this could be done sooner rather than waiting another year?
I would say go for it - change your name ASAP and get started