Where would I put a name suffix on an I9 form or any form that doesn't have a specific box for a name suffix? On this form I only see fields for Last Name, First Name, Middle Initial and Other Last Names. Is it necessary to provide a name suffix on forms like this and if so where would you recommend placing it?
The SSN is the primary identifier. The name serves to prevent someone without work authorization from writing down a random nine digit number.
The standard is that when the employer inspects the documents (your photo ID, proof of citizenship, and the I9 form) together, they should "reasonably appear to relate".
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
Then you should 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.
Including or omitting a generational suffix is not going to cause you to fail this test.