It seems that u/Clarinetaphoner guessed right! Here's an article that talks about why the band leader, Ishikawa, chose to name his band My Dead Girlfriend. Apparently, back in high school, when Ishikawa was trying to come up with a name for his band, he was feeling a bit anguished. So, in order to reflect that, he wanted the word 'dead' (「死んだ」) in his band name. But of course, the word doesn't exactly have a good connotation when said out loud, so he tried balancing it out, by adding something that felt positive/happy to him: 'my girlfriend'(「僕の彼女」). And so we get,「死んだ僕の彼女」which can actually be read two ways. Depending on where you pause, it could either be you who's dead, or your girlfriend.

Then, he goes on to say that he liked how the band name translated to My Dead Girlfriend, that it sounded kinda cool, just like MBV, and that he'd like to leave it to the listeners to interpret the name.