My friend often sands me links from the Duomi music service. Where does the name come from? 多米 seems to mean "a lot of rice" if I translate it directly.
My guess is that it comes from the musical scale DO-re-MI in English. Googling didn’t turn up a standard way to transliterate this – someone used 豆, which may be closer to the English sound, but the more positive connotations of 多 might have led the person coining the name to opt for that instead. Anyway, 豆米 sounds like some kind of Taiwanese dessert, not the right fit for a music website! :)
First off, 山寨 (to bootleg, to rip off, to knockoff, to imitate (as in imitation goods)) is one of the most common things that you will find in China and from Chinese people.
For instance: Pizza Hut (必胜客) has been 山寨ed by a company called 必胜宅 - if you look at the characters there pretty much the same, even the meaning of the changed character is very similar! The products the fake Pizza Hut makes is pretty much the same as Pizza Hut, basically just a knockoff with Pizza Hut stuff. There's tons of similar examples of Chinese-style 山寨ing.
虾米 is one of the most popular music services in the Chinese speaking world, at the moment. Why they named their service that, I would assume is just because around the time of their starting 虾米 was a super popular way to say "什么" (What?) - so they just grabbed on to some faddish thing to draw attention to their company.
多米呢? What about 多米?
Well this all comes back to 山寨. If you want to 山寨 something, first, you pick the most popular brand of whatever you want to 山寨 (in this case 虾米) and copy their name. So 虾米 - 多米. The nice thing about 多 here is that their name seems to "one-up" the original - they've made it sound like they are the same as 虾米 but, one, have more (stuff, features, etc.) and, two, are better: 多. All that just from the name alone.