What you need to know is Brand Architecture. There are potentially 3 types of brand architectures which is nothing but a framework into which its brands fall.
Your question has more than one brand architecture.
Virgin brand follows "Corporate or Monolithic" Brand Identity where its sub brands share the same first name. Subsidiary is a very generic term to define any brands under a parent company. I would perhaps call it a legal term.
Your other example is Violetta by Mango is a classic example of "Endorsed" Brand Identity. It can either be endorsed by a group name or visual style (Ex. IKEA and LIDL)
The last type in this architecture is "Branded" brand based identity. This happens when companies separate their identities as corporations from those of the brands which they market. Example Unilever which owns Dove, Ponds, etc; all of which have separate brand identities.
Now, coming back to your question. What do you call this when a brand does to its logo?
You can call these brands as sub brands or brand extensions.
Source: Wally Olins 2008