Name Change and Jobs

A couple of months ago, I legally changed my name. 
I thought this would be a relatively simple process, pay a stupid amount of money, get a new birth certificate and bam the dirt is gone.
Since that time, I have learned there are so many frustrating little road blocks that trans people have to overcome, just to be recognised as who they are. 
One of those challenges has come up recently as I have been looking for a new job. 
I have only had one job under my current name, all my old employers know me as by my old name.
So what do I put on my resume?
If I need referees, who can I put down? 
Does it look bad for a 23 year old to only have a work history of one job?
If I tell my new potential employer, I have to out myself before I have even met these people.
They could then go on to out me to my old employers. 
It's kind of like we're fucked whatever we do.