I would go with the addition of a surname, it does make a difference and (most) clients can then know which Amy, Anna, Emma, Lucy, Jas they are talking about.
Or you could add something at the beginning. Kinky, naughty, flirty etc.
Every other Indian escort seems to be called Jas, Jasmine etc. So to stand out from them I just added naughty before Jas. And now I get some clients that phone up and ask for Naughy Jas! So it does work. Besides you now what they say, naughty by name, naughty by nature.