Yes - to be honest, I'd been wondering why some clients ask me frantically, "Are you discreet?!?!" and always felt like replying, "Er, I'm going to wear a t-shirt that says WHORE VISITING MR SMITH IN ROOM 123 on it, am I?!" But now I see that maybe he's just worried I'm going to go talking to the hotel staff on reception!
I would never ask for a key to a client's room, and if I were stopped by hotel staff asking where I was going (highly unlikely, but still could happen in some place with odd management) I wouldn't say the client's name, room number or call him in front of them. I'd say I was visiting a friend and if they have a problem with that, I'll just ring my friend and ask if he minds coming down to meet me. Then I'd go somewhere I could make the call privately and explain to the client, giving him the choice of whether to come down or just call the booking off. I don't care who knows what I'm doing, really, since I can always just never go back there and nobody can prove anything anyway - but telling hotel staff which guest is receiving an escort this evening is best avoided, isn't it??
I'm pretty sure 90% of guys staying in a hotel would be absolutely mortified to know an escort asked for a copy of their room key at reception! What if his wife came by the next day to do the same thing and a careless receptionist said, "Oh, are you sure you're his wife? Can I see your ID, please? Because you looked very different yesterday!"
Divorce o'clock.

(Obviously if you agree with the client in advance that you'll get a room key from reception then that's completely different, so apologies if I misunderstood.)