I don't hate it, but it is a bit weird, due to it being two ranks from the Elite Pilot's Federation (I know there's the lore explanation about allowing Dangerous pilots to take Elite jobs). There's just something great about the original purity of the simple name, "Elite".
Having said that, it's better than names for certain other upcoming space sims, partly due to its heritage, partly because the first alternative sounds more like a government simulator and the second alternative seems a bit backward with an emphasis on one gender built in the name.
Didn't someone find out that "Elite: Deadly" got copyrighted by Frontier? That could mean the name is going to change over time. Though I don't know where it could go from there - "Elite: Elite" is a bit silly. Elite squared?
I think a good final name might be something more general... like Elite Galaxy. Maybe people would stop talking about it being about erectile dysfunction then
Elite: Frontiers would be pretty nice too.