They're not getting rid of the Android brand... Not sure how or why people came up with that? They're just re-branding the store within which Android Apps are sold. This is a good thing for several reasons:
1. I'd say first and foremost changing the name to Google Play promotes the idea that it's not JUST for Android. It doesn't matter if you have a Mac, a PC, a Linux box.... Google is providing the same thing they do with Gmail. A one stop shop, you can get your music, your books, your videos... It's not just for Android. It's universal. (I noticed a LOT of Apple users suddenly logging on to the store and checking out what they can buy/download, etc...)
2. It pulls it together under one moniker. It's not several different brands they have to support/promote. Instead of Google Books, Google Music, Google Movies, etc... Now it's just Google play and they can market it all together. It eliminates a mental step for users as well. Where can I get that... Google Play! (It works well for iTunes, and Amazon) They could have called it Market but:
3. Play DOES signify a fun atmosphere. It's not just a store. It's a place you want to hang out, it's fun. This is very important when selling stuff like music and movies.
4. Play is also a word people enjoy. People like to play. I can almost bet they're hoping that we start to associate that with shopping at their store, just like people eventually just started "Googling" things instead of searching for them.
As for it not being very business like. I really don't think that matters. Business Tech is starting to swing towards user driven. Instead of the IT Dept telling you what phone you can have, the user tells the IT dept what phone they have, and want to use. If they can capture you outside of work, you're more likely to use it for work as well.