What’s the explanation for this type of name given to many of the big government-backed lenders?
FWIW, I used to work for a unit of Sallie Mae. No one at my small office could answer that question for me. I assumed it was just derived from the way the actual acronym came out: ‘SLMA’ (standing for ‘Student Loan Marketing Association’). Say that a few times fast and it starts to sound like 'Sallie Mae".
Take Federal National Mortgage Association.
or, FNMA. Say FNMA fast. Say it often enough and pretty soon it’s “Fannie Mae.” This, to my limited knowledge, was the first one, and started the trend.
Sallie Mae: Student Loan Marketing Association, or SLMA. Say SLMA fast. Say it often enough and pretty soon it’s “Sallie Mae.” And so on. Some, like “Freddie Mac”, don’t match up; I suppose they just got the names to keep up the cutesy tradition.
“Fannie Mae” and “Ginne Mae” are, respectively, FNMA (Federal National Mortgage Association) and GNMA (Government National Mortgage Association). Fannie Mae is a private corporation, while Ginnie Mae remains part of the US Dept. of Housing and Urban Development. The pronunciation seems logical, given the initials.
As for Freddie Mac (FHLMC, Federal Home Loan Mortgage Corporation), I have no clue how that pronunciation got started, unless it was to somehow give Fannie Mae and Ginnie Mae a Big Brother to watch over them (pun intended).
Freddie Mac? Isn’t that that Black comedian with a show on Fox? 
Bernie Mac’s real name, of course, is British National Mortgage Corp.
Here is an article from Slate that describes what Freddie Mac (Federal Home Loan Mortgage Corp. (FHLMC)) and Fannie Mae (Federal National Mortgage Association (FNMA)) do. It also includes an explanation for the name–basically that Freddie=Fed and Mac=MC
My wife works for Fannie Mae. Several years ago the nickname became so common, they officially rebranded themselves as Fannie Mae. (Note the spelling vs. Fanny May.) When my wife says where she works, occasionally someone says, “I love those chocolates!”
P.S. Fanny May