Dear Allan Jordan/"A. E. Jordan",
I have not contacted the court involved with my grandfather's name change -- and have not found the name change file.
(I'm not as diligent as many other with respect to genealogy.)
I do not quite understand what you said in your final paragraph with respect to the New York City Department of Health and birth certificates: I'm not (myself) certain that it could be said that the birth certificate was "reissued" (as I stated, I saw on the microfilm the original certificate with some material added (mostly as hand-stamped text).
My research at Ancestry.com (and my impression from what little my father said about this when he was alive) lead me to believe that although (legally) the name change had been completed by September of 1940, neither my grandfather, my grandmother (who probably never used the name "Kent" for herself), nor my father or his 2 brothers publicly used "Kent" until at least 1948 -- so I suspect (although I do not know) that my grandfather (or a lawyer representing him) contacted the Health Department when he finally decided to publicly use his new name -- and that that is what prompted the Health Department to amend the birth certificate to what I saw on the microfilm a few years ago (not "they needed it for something [unspecified] else", then).
Ethan W. Kent
New York City.