european living and working in the UK for under 6 years

InesBC

I would like to know my credit score but I have only started living (and working) in the UK since February 2020. I had an Amex card for 1 year, but I am afraid this has not counted towards my credit score. Another issue that I frequently have with bank accounts etc is that my legal name is longer than most forms accept (I have 4 legal surnames and 1 first name). 
Has anyone encountered similar issues? 

born_again

In the UK. your score is a meaning less figure made up by the credit ref agencies. It is not seen by any lender.
All you need to worry about is your credit history. So paying bills on time.
Any application for credit is viewed on history & then lenders own internal scoring/credit risk/appetite for debt.

As to name issue. It maybe worthwhile speaking to any bank on how they would like your name format. 

Shanwick

Have you tried accessing any of the free online credit file sources?

https://www.moneysavingexpert.com/loans/check-free-credit-report/

Your credit file may be too "thin" to permit online identity verification. If that is the case you can contact the CRA directly to obtain a copy of your file by mail.

PRAISETHESUN

As above, ignore the focus on "credit scores" and the like. They are a marketing gimmick and are not used by lenders to decide your creditworthiness. Instead you need to check the actual data on your credit reports, to see if it is being recorded accurately.

I had similar issues getting access to my files when I moved to the UK. My advice would be to contact each of the 3 CRAs (Experian, Equifax and TransUnion) to request copies of your "statutory credit report" under GDPR laws. It's likely they will request copies of ID documents - provide these (or offer to provide them if they don't ask for them) and you should then have access to your credit reports. I found once I verified myself the first time, I was then able to access my files online on a continuous basis.