Is it possible to rename SharePoint 2013's storage to something a bit easier for end-users to understand?

When have on-premises SharePoint and the storage area was originally called SkyDrive Pro, abbreviated to SkyDrive. This was confusing because Microsoft's publicly available service was also called SkyDrive.

Then with SP1, they re-branded it to OneDrive for Business, abbreviated to OneDrive. 'Excellent news' I though, 'that will save confusion'. But then I realised the publicly available SkyDrive has also undergone re-branding, it's now called OneDrive too!

This is a nightmare for our teachers who use a personal OneDrive/SkyDrive to understand. 'I uploaded a file to my OneDrive, but when I click on OneDrive in school it's not there'. I have to explain that there are actually two OneDrive's, both called OneDrive, but containing different files in two different places.

Has anyone been able to rename it without having to hack around with SharePoint too much?