Differences in name

Hello Everyone.

I applied for an ALT job in Japan. Most of my document, such as my birth certificate, ID details and so on include my first name, middle name and last name while my Bachelor's degree certificate and Proof of English Proficiency has just my first name and last name and and this was due to a name omission done while registering to the university.

Will this hinder me from getting the job and other necessary paper work or can a legal affidavit and legal correction of name help solve the problem?

No that should be fine. I don’t think my documents contain second and third name either. (Actually in my case it is even more complicated. I have 3 first names but use the last one of those. And have a lot of documents that don’t include the other 2)
Only official documents (passport, driving license type of documents ) contain all my first names.