Over the years, I've done a lot of hiring of folks with similar names.
I never care about the name. I usually care about the ability or lack of ability to work without sponsorship. If I'm not able to offer a sponsorship for a particular position, I note that in the job description, and always ask about it during the phone screen.
What has been most useful to me has been to see somewhere on the resume that the candidate is a US citizen. I'm looking at a resume as I type this. The very last line simply says "US Citizen". That works fine for me.