I am assuming that Form 10-Q stands for quarterly, though I can't derive a good reason for the 10.
The name of the Form 10-K comes from the Code of Federal Regulations (CFR) designation of the form pursuant to sections 13 and 15(d) of the Securities Exchange Act of 1934 as amended.
But I couldn't find it on this law site. And I am not well-informed about the structuring of laws and have no idea if these numbers are even representing "sections".
So does anyone have an idea where the terms come from?
Sidenote (unrelated): Probably I could ask this in the English SE as well, but I'll leave it here for now.