Should I change my name on the degree?

Hi, so I’ll be graduating soon and I always wondered if I change it to my full legal name?
Like basically let’s use an example my name is “mark John Wood hill” because I’m from Spain they use father and mother surnames. I move to uk and since high school, because of my name being too long they technically shortened it to “mark wood” even in college it was shortened to mark wood like on my ID CARD etc. ofc I’ve provided my details to them passport etc, but it’s done automatic now. And now in uni, because it’s always been “mark wood” in academic setting, I put my name as mark wood. But ofc on my bank etc, it’s my full legal name.
I just want to ask, because the degree it’s a public record technically and a big thing, should I make sure it displays my full legal name? So in the future it doesn’t cause me any problems? Or would mark wood would also be fine as that’s what I’m known as. I just don’t want it to be a future problem when employers think im someone else, as my name is kinda different on the passport etc.
Btw my name is not mark wood, but everything else is true. Plsss I need help. On what to do, and what’s the best decision to take. Because if I do change my name, then on my other sixth form and school certificates, it only says “mark wood” on them. So those would look different then. Pls help

I would make sure your university issues your degree certificate with your full name, as shown on your identity documents. Then there's no question as to it being a degree that was awarded to you.
Does your university have your full name on its records already? In many cases organisations do use your preferred name in most cases even if it's different from what your birth certificate/passport/other identity documents have. But they would normally issue formal documents (e.g. degree certificate) in your full name.

What is the name format in your passport and similar documents?

Yeah on my bank, and passport etc, it has the full legal name. Because most of those documents were issued in Spain and it’s been carrying like this. Even at my work, it has full legal name which ofc makes sense. It’s just that in my school, uni, sixth form… has the short name.