Residency card Application- Help please

[Sabara]

Hello all.
I have an important question for you all (hopefully some will be able to help)
I have been a UK resident for 19 years. I am originally from Spain.
Since entering the UK I have continuously worked and then I went to University. For the last 10 years I have been in full time employment with the NHS (without a break, so I believe this qualifies me straight).
However, as a spaniard, I have two surnames. When I arrived in London my NI, bank account, bills, everything was placed under my name and my first surname (I was told this is the way as in the UK people either have one surname or a combined surname such as smith-walters). All my documentation has only Name + one surname. Even my UK university degree, my NHS number, my work, my p60's... everything.
Now I am in the process of applying for a UK residency card and I am very concerned that this will give me problems for verification or identification purposes and that my application may get rejected.
Anyone out there that has been in the same situation?
Any help or advice will be very appreciated.
Thank you all and good luck today with the elections!