What is my name in Chinese (full form and 3-character form)?

My name in English is David Otto. I have some questions with regards to how to write my name in Chinese.

Looking at a dictionary, "David" is 大卫 and "Otto" is 奥托, but I wonder if I were to write my full form name in Chinese, whether it would go 奥托 大卫 (surname first, as normal Chinese names go) or 大卫 奥托 (surname last, as people in anglophone countries say and Chinese people may want to imitate). Which way is more common for writing Western names in China?

I would also like a Chinese-style three-character name. My part-Chinese girlfriend insists that I just use 大卫 as anything else would just sound weird, and maybe she has a point. Nonetheless, I'm sure there are many Daweis in China already and I'd still like to have a character to represent my surname.

She says 托 大卫 and 奥 大卫 sound strange. Does anyone have a suggestion that either sounds vaguely like "Otto" or means "wealth" (the original meaning of the name)? Thank you.