Providing my full name helps preempt the sometimes uncomfortable "what are you?" that people wonder when they meet me because I'm multi-racial. But, I find using my full name to be unnecessarily formal, so I usually avoid it.
But, what if I'm submitting a resume through a structured recruiting process? Should I include my middle name? The unfortunate reality is that studies show people have vastly different response rates when submitting the exact same resume using different names - worse response rates for minorities.
Idealistically, I'd be able to submit a resume without my name on it. But, since that's not socially acceptable, I try to minimize the attention that can be drawn to my racial background. So, I leave out my middle name. I'd prefer a company focus on whether they think I'd be a valuable addition to their team.