This isn't a definitive answer, so much as a research dump, but perhaps it may help someone else come up with one.
It appears that the site was "discovered" (archeologically that is) in 1974 by the late French Archeologist Jean-Francois Jarrige. Its possible there's an interview somewhere where he discusses the rationale for the name, or its in his first report about the site, but most likely that would be in French, which I am not fluent in.
The best English-language source about the discovery of the site itself I could find online was an Ancient Origins website that said this about the name:
In the native Balochi language, ‘mehr’ is said to mean ‘love’, and
‘garh’ means heaven. Thus, the name of the site may be taken to mean
‘the heaven of love’.
Putting this statement in there seems to strongly imply that the name was given by locals, but nowhere is this flat-out stated. (I'm also pretty dubious about the translation given in the second sentence, but probably nobody on earth knows the Balochi language less than I do, so I'm in no position to judge).
According to Unesco:
Following its abandonment it was covered by alluvial selts until it
was exposed following a flash flood in the 1970s.
From this little bit of information, and what else I know about how sites tend to be "discovered", my best guess would be the following: The site was found by Balochi locals after said flash flood, and eventually Dr. Jarringe's team heard about it and went to check it out in 1974. The locals likely guessed it was some kind of ancient holy site, so amongst themselves they had already given it that "love-heaven" name.
Its possible the "love" part came from some of the figurines found there, pictures of which would be NSFW, as they seem to my prudish modern American eyes to be sexualized.
That's just a guess, based on incomplete information though.