I have a pen name for my sweet romances. All my correspondence is done under my legal name. I'm independent, no agent.
When you get a phone call with an agent about your first book, that's the time to bring up your other genre. Ask the agent how much experience she has with thrillers and whether she'd be willing to represent that one, too, or if she's got someone else in her agency who would handle those books. You aren't the first author to be writing in disparate genres, so the agent has most likely dealt with this question before.
If they're both ready to go at the same time, then start querying the second manuscript to a second set of agents, and again--ask what they'd do about the first one.