An acronym. The "GPP" is the DOS-ified spelling of "g++"; the '+' was not (officially) allowed in MS-DOS filenames. The DJ stands for the first name (not the initials, apparently [1]) of the project's originator, DJ Delorie.
Although: "Since C++ is integral to gcc, djgpp no longer stands for "DJ's G++" but probably stands for something like "DJ's GNU Programming Platform"." [2]
DOS:
"One of our commands allows separation of filenames with a + symbol, so we need to prohibit that character."
"Couldn't we rework that command to not use + separators?"
"No, far better to take that character out of consideration."
Unix:
"Filenames can use control characters. I don't care if that makes pipes between commands really complicated! Add an option for NUL-separated filenames if you have to."
Additionally, word-initial single G before short I is always [g] instead of [dʒ] in native English: gift girl give gibbon gimlet gizzard gilded git gimp giddy gig gimbal.
The exceptions are
borrowed French words: gin (le gin), ginger (le gingembre), giraffe (la girafe), giblet (OF: gibelet).
I personally follow the "I am the user, my rules" when it comes to language rules :P. It is at least as strong as "their word, their rules".
Also I can see that Paul Graham's "my website my rules" is even stronger than mine or DJ Delorie's, so Djgpp is also correct (if not by the Gods, then by fist).
Although: "Since C++ is integral to gcc, djgpp no longer stands for "DJ's G++" but probably stands for something like "DJ's GNU Programming Platform"." [2]
[1] https://www.delorie.com/users/dj/
[2] https://www.delorie.com/djgpp/history.html