In the UK one used to be able to be called whatever you wanted. Only your birth certificate had your "real name". Actually, there was no "real name" and you could go by any name you wanted.
Then two things happend, the Soham Murders (two school girls murdered by someone where the Police and others had intelligence that he had been naughty in the past, but no way of sharing it) and the War on Terror.
Somehow, these resulted in the government wanting to bring in ID cards, which failed. But another effect was a clamp down on money laundering meaning one can only open a bank account for a proven identity.
Until about 2002 one could open a bank account in any name at all. Not any more. The government forced the banks to bring in a load of ridiculously strict rules before an account could be opened.
In 2003 or 2004 NatWest made an error and closed all my and my wife's bank accounts. Because we had no paperwork in her name (I paid the bills) she could not open an account anywhere, despite having a driving licence and a passport. Those were in her full, 3-part name, but her previous bank accounts were in her 2-part name.
My wife went without any bank account at all for about 3 years, because she could not get one. To fix it we had to get letting agreements in her name plus get electricity and gas and telephone bills transferred to her. Eventually, because there were millions of people without bank accounts - specially school leavers and people leaving home - the rules had to be relaxed enough so she could get a bank account of her own.
Anyway, since then the government has realised that because a bank account is now definitely associated with a person, they can get the Inland Revenue to snoop into them to see if people's income matches the tax they are paying, so the government likes it that way. Because of that, banks have to use your full name.
Note that the credit checking agencies will have you down as both P S H and as S H and will know they are the same person. They are very used to people using multiple names.
As for any other organisation, it is down to them. Anyone who gives you credit without checking your full name is foolish, so they care. But what difference does it make to utilities or most other organisations? They either know where you live or they have your bank details.
I suggest you make sure your university puts your full name on your degree certificate so that it matches your birth certificate and passport. It will make getting a job easier if everything matches. But by all means tell that new employer you don't use your first name and they can set you up using whatever name you want. They will probably have your full name on any paperwork that goes to the Inland Revenue, but it doesn't matter if they don't - it's the numbers that matter, not your name.
Most (all?) central government systems now handle aliases - the Disclosure and Barring Service, the Police, the Prison Service and I expect most others will let you have more than one name and know it is all the same person.
The Electoral Register doesn't matter much which name you use, and Council Tax systems don't care so long as you pay up and the NHS don't care.
In reality, you're only a number on a database anyway these days.