What is the name of this grammatical phenomenon?

Solution 1:

As a figure of speech, this is called anacoluthon—when you break the grammatical structure of a sentence and begin a new construction or a fragment of a construction. This Greek word means "that which does not follow". The term is less used outside of a literary context, but it is the same phaenomenon.

It is commonly indicated in writing by a dash (although not all dashes indicate an anacoluthon: they can also be used for parenthesis, which means that the grammar is only temporarily interrupted, to be resumed afterwards).

I have to say, though, that your example strikes me as ugly. A good anacoluthon is used for rhetorical effect; when that is not the case, it is often simply considered an error. As to when it is considered an error and when it's not, that is very difficult to define.