Microsoft has announced that Xbox Music will become Groove going forward, whilst Xbox Video will become plain old Movies & TV. The reasoning being that Microsoft discovered users who didn't have an Xbox thought the service wasn't available to them.
I can't see this as a naming issue though. Dumping a strong brand like Xbox from its services doesn't make a whole lot of sense anyway, but doing it for a self-inflicted reason is a very bad move.
Microsoft have all but kept the Xbox Music service a secret. Promotion has been non-existent since the Zune branding was stripped away. Whilst that move made some sense - the Zune's market failure was toxic to the associated music service's brand, the move away from Xbox doesn't have the same driver.
A far more sensible option would have been to make a big splash about Xbox Music, perhaps matching Apple's three month free trial with a similar offer. Most importantly making people aware that the service exists and also works on just about any hardware you care to mention.
Instead we have yet another Microsoft brand with no history and no name recognition (and potentially another lawsuit over the use of an existing product name). This rapid cycling through sub-brands doesn't strike me as a great business strategy. Hopefully though Groove will be given a bit more support in the market than Xbox Music ever was.