On the couple of occassions I've flown to see a client, 1 was a trusted and respected client within the BBW community, and I'd seen him a few times before, so on that occasion I didn't mind giving him my real name to book the ticket with.
But on the other occasion, although the customer had seen a friend of mine, this would've been the first time I myself had seen him, so I wasn't totally comfortable. I looked up the airfare myself and sent a link to the customer so he could see how much the fare was, and I had him transfer the fare to my bank account so I could book the ticket myself. It's a little account where nothing much goes in. That might be an option to consider.
Mind you, things may have changed slightly now, that was a few years ago. Back then he didn't have to have my name to deposit the money. Just my sort code and account. I'm not sure now.