In the UK, it’s really easy, as both first names and surnames can be changed with a deed poll. This is basically a document that details your new and old name, signed by two people that aren’t related to you that you have known for at least two years. We don’t really have defined “legal names” here, so the deed poll is accepted by most organisations to change your records (PayPal were weirdly annoying about it, even after I’d changed my driving licence and passport with zero fuss.)