What is correct MVM vs. MMV?
According to the International Committee on Taxonomy of Viruses, it has had several official variations of that name over the years:


Minute mouse virus
Minute of mice virus
MVM Virus
Minute virus of mice
Mice minute virus


The current (2014) accepted name is: Rodent protoparvovirus 1

"Does it really matter?" As long as you write in full the name you're using the first time you use it, people will know what you're talking about. However, for consistency amongst current literature, perhaps we should all strive to keep up with current taxonomy.