So even the service names are going for the lame "simplified" rebrand that has been so popular over the last few years.
Re: reasons why. I figure there are three possible reasons, or some combo of the lot.
1) Trademark. Some markets might have had it, EA App might be trademarkable where Origin is harder or potentially some other company/market they cared about. Some marketing type might also have done a scan and found everybody in the world regardless of language knows App where Origin is an English word so eh. I can't imagine they did not own what they could everywhere either (if the name was loaned out to some company then eh, see Harvest Moon vs Story of Seasons for a similar one albeit the reverse as it was the localisation company that owned Harvest Moon and they wanted to switch up from them).
2) Bad PR. Don't think it was the case here, certainly not enough for EA to care, but rebrand in the face of it to trick people is a thing done many times in the past.
3) Some accounting reason. Where I would put my money. Some accountant somewhere totalled up some kind of unfunded liability list (if you have to provide support and downloads for all these purchases) and found it wanting. Deadlining a service might be hard as you have to provide support for however many years since last sale. Rebrand to totally not Origin (maybe the slimes in product research that could not even hack it in marketing or HR came back with "everybody understands App"/"App is the cool new word of 2012 and we will be down with the kids" so go with that) and you can start that last sale clock, phase it out of memory.
Unfunded liability could also run into technical issue -- see shuttering of original xbox xbox live back when as it was at some level "holding back" the 360 (granted I would call that a non issue/convenient excuse). I don't think EA are maintaining a legacy version for Windows Phone or anything.
We will probably never know which those are the main reasons for a rebrand.