I don't know how I feel about this name. I love the meaning and connection behind it, but the harshness of the first syllable kinda turns me off. I'm not sure. I think I'd have to meet a Gethsemane in real life to form a strong opinion.
There is just something about Gethsemane that really strikes me as beautiful. To me it has similar qualities to Galadriel: it has an elegance, a graceful flow.