[JAS84]

Yeah, the name Strictly Come Dancing is a combination of the names Strictly Ballroom and Come Dancing. Outside the UK, Come Dancing is an unknown brand, so they dropped the reference to Strictly Ballroom and just went with a name that's exactly what it says on the tin.

Quite like this graphic of the layers to the rebrand: i.imgur.com 

That graphic is from November last year at the latest - because that's when the new Doctor Who logo was revealed, and the graphic has the previous one on it. So, yes, definitely also before the kids channels' new logos were created. Though you'd think they'd have just used the old ones.