Help: Name mismatch issues

I am facing issues in getting my DL in NJ because of name mismatches between I94 and SSN. Anybody else face the same situtation?

My Name in the I94 is
Last Name: <13 Letters> <11 Letters>
First Name: <6 Letters>

In My SSN,
Last Name: <13 Letters> <6 Letters>
First Name: <6 Letters>

Basically, my last name is stripped off because its longer than 20chars. Will this cause an issue with DMV name mismatches? Any idea what i need to do now? Do i need to get the I94 corrected to have a middle name so that it fits?