I didn't even notice the mistake at first -- my name is not misspelled, so I figured if I didn't say anything I would be able to get away with it. I knew my EAD card would have to be photocopied or scanned at some point when I first arrived at the office, so I crafted some inane plan to tell an engaging story while the HR person was taking care of my documents, in the hopes they wouldn't see. In the end no one ever noticed, I ended up getting H1B a few months later. But I don't think my worrying was unfounded; I'd heard stories of a single character being wrong (or, missing an accent, and therefore not matching their passport) and someone's entire life changing (they had to go back to their home country).

I should also note that the guidelines for filling out CPT and OPT are also completely nebulous. I forget what the specific issue was, but I remember the administrator at my university being unsure of how to answer some question, them having no recourse, and me having nobody to ask.

I'm on my 4th year of H1B and I need to figure out how to apply for a GC. The time investment in putting together all the documents is significant. Not to mention exiting the country to go see loved ones is always a pain.

I think the name switch is unlikely to get you into trouble. My country has the reverse of the US (First name is last name and last name is first!). I've been switching regularly and this only confused people who wanted to address me by my "first name".