It seems there are a lot of different approaches to this.
If someone was listed by a nickname in documents such as the census or BMD records, I'll put that nickname in quotes, e.g. Elizabeth 'Betsy' Oliver.
An exception to that rule: my great-grandmother was named Isabella Grace but was identified as Jane in every census record with her parents. She wasn't called Jane as an adult (according to her grandchildren) and it isn't on any official documents that I've found. So I mentioned it in the 'notes' section for her entry but didn't put Jane in quotes as part of her given name.
If someone in Scotland had a name that was interchangeable with another name, and both names were used on different documents, I'll write it as Jean/Jane Oliver, for example.
If there were multiple different spellings of a surname, I'll pick one and stick with that, but any transcripts I make of individual documents will be accurate and stick to the source, however the name may have been recorded, e.g. Currer, Curror, Currar, Currier or Currie.
In my own life, I've always been called by my middle name, but official government documents insist on identifying me by my first name (it's the rule: everything must match), so sometimes a doctor's office will have my full name on a file, but they'll underline my middle name to indicate that's what they should call me. I can't do that on my genealogy file (I use Reunion 11 for the Mac) where I enter the names but I could do it in any print-outs or in the notes facility.
Regards,
Josephine
P.S. In cases of people using a surname they weren't given at birth (usually a step-father's surname), I'll record them as SMITH a.k.a. OLIVER.