The name on my birth certificate is XXX YYY. The name in my first passport/visa I came to the USA on is YYY XXXA ZZZ (ZZZ is my fathers last name however it doesn't appear on my birth certificate) which switches my first and middle names and misspells my transposed first name. I used that passport throughout school in the USA but had my social security number as XXXO YYY ZZZ. During that time my name on my I-20 was XXXO YYY ZZZ which conflicted my visa/passport but never had a problem at immigration/airport when I presented both.
At my permanent residence interview, the officer declared my name ought to be XXX YYY ZZZ and issued my permanent resident card in that name and when I recently naturalized, I've continued with that. I have never had any court/legal documents documenting these variations.
On the USCIS website it says:
"We know from experience that records of entry of many aliens into the
United States contain assumed or incorrect names and other errors."
Additionally USCIS in official direction to employers says:
If your employee Presents a document from the List of Acceptable
Documents in which his or her name is spelled slightly differently
than the name he or she wrote in Section 1, Ask your employee the
reason for the difference in spelling. If it reasonably appears to be
genuine and to relate to the individual, you may accept the
document.
Clearly this kind of discrepancy happens more than you would think. You should be fine.
