Many Goths take on different names or a persona. It is not a requirement of the goth scene, you can keep your regular name.
Goths can take up a goth name because they don't like their name and wish to change it or another person dubbed them something and wish to keep it.
I know for a fact my friend Jannice and I discussed the subject once and she told me about how she wishes to change her name to 'Raven'. We then went on to discuss goth names we would like to adopt. I said I wouldn't mind being called 'Talon' since I have such long nails and everybody notices and comments on them (I will post a picture in the future when I grown them again), but said I felt a goth name must be given by someone else.
And that is why I've changed my to The Princess of Darkness. My boyfriend has called me this along with many others and some people call me this as well or have added their own names to my ever growing mental list.
Of course if you don't want to wait for someone to call a goth name, you can always look one up for yourself and make the change. Trust me, there are A LOT of sites out there.
Ill give you some help though, if you want a goth name.
Goth Names for Girls:
Raven (can also be spelled Raeven, Ravyen, Raiven)
or anything starting with "Mistress", "Lady", etc
Goth Names for Guys:
Damien (or Damian)
or any bloody sounding name or demon names
Of course these are just a few suggestions. There are many names out there. Look them up, im sure you will find one to your liking.