"Game Boy" suggests a product for males and young people. The DS attracted middle-aged adults and females much more than any system before it. And while I think some of the specific titles like Brain Age and Nintendogs are largely responsible for that, I'm sure marketing folks at Nintendo are tooting their own horns about switching to a gender and age neutral naming convention. I doubt they'll ever go back to the Game Boy name.
"Game Boy" and "DS" are also both associated with handhelds, just like "NES" or "Wii" are associated with consoles. Nintendo probably doesn't want the Switch to be associated as either one or the other since it's both. This is something new, potentially for all of videogames, where it is just a videogame system and you use it in the way that suits your life. That is an ideal time for a new naming convention.