Study in UK with my EU-ID? Got BSc diploma from a non-EU country with my non-EU ID?

Hello as the title is complex so the situation is:

I was born in an EU country in 83, had to immigrate to a non-EU country in 89, having a different name on my non-EU ID. Studied university in non-EU country, however I want to apply to postgraduate studies in Europe with my EU-ID.

Problem: on my BSc diploma, which I got from the non-EU country has my non-EU citizenship name on it and my EU citizenship name is different. Reason is, the legislation is different between two countries, in EU country it doesnt works like first name - surname, it works like first name - father's name - grandfather's name thus they do not use a specific surname but combine fathers and grandfathes name to complete a name of person.
Just to formulate:
*My full name in non-EU country: AAA BBBBB where BBBBB is the surname we chose during immigration
*My full name in EU country: AAA XXXX YYY where xxxx is my father's name, and yyy is my grandfather's name.

I hold valid documents from both governments stating that AAA BBBB = AAA XXXX YYY and it is the same person.

So under this circumstance, am I eligible to apply schools in Europe with my EU-ID? I'd really appreciate your answer since I couldn't find any info about this on the internet.

Thank you.

[annjd]

You may need to get a court order that clarifies and confirms the documents and gives the force of law to your papers.

There may be concerns of fraud if you cannot do that.