This would also seem to put his first employment, at Sears, in 1940 rather than 1939 as has been written in the bios. He was unemployed when he filled out this form, and most employers, especially a large company like Sears, would need a social security number to put you on the payroll (or they would apply for the number for you).
When I bought my first house, they REQUIRED me to sign my full name, not my legal signature, including the "jr", which I never use, It is odd. They required the same thing of the 20 year old Hank in 1941. That is not necessarily his signature. It is a cursive writing of his name. My legal signature looks like a big loopy BRRS, but for some companies and government agencies, that it not good enough. I'm not sure how they would handle it is I was illiterate. An X used to be good enough for a signature, not requiring someone to write out their full legal name in cursive...
You could tell how they were busting his balls in the way that they made him write the address. Notice that he wrote L A, CA and they make him write "os ngeles" next to it. ha!
He may not have known how it was spelled. I didn't know how to spell my mother's maiden name until after she died. I just never saw it in print, never saw the birth certificate, marriage certificate, wherever it was I finally saw it.