I was born in other country and I went to university there. They gave me my university degree with the name I was born with. Years later I became American by naturalisation and I chose a new name as new American citizen. But my degree title has the other name, not the one I chose in America.
In the (unlikely) event that you are asked to provide an employer with a copy of your degree certificate during a job application, you just include a copy of your naturalization paperwork showing the name change.
I think if you explain your situation when you apply. Then, if the college of your choice does not accept your credeintials, try apply to another college.
Good luck. I was a college professor and admissions chairman at a larger university.
Should first check out to see if that degree will even be recognized in the US, many are not. Depending on that answer determines whether jumping through the hoops is worth it or not.