Start right now where you are
Don't wait for a new name.
I always post this link, but this is what got me started and I still benefit from the simple practice it describes today.http://www.urbandharma.org/udharma4/mpe.html
That said, I think you usually receive a Dharma name when you formally take refuge for the first time.
That's not something you normally do right off the bat.
Good luck and welcome to Dharma Wheel!