This is a tough one for me as I even don't know a German word for it. A company can have a logo (an easy remembered image). If it goes radio, it can have a jingle (an easy remembered melody). Now what is the word for a small video (especially for a movie company, occuring at the start of all their films)? E.g. the MGM lion. Googling for that it autocompleted to "MGM lion intro", and the word is in wide use. M'kay, but this surely isn't the "technical" phrase for it?!
I one of the questions here is whether a "logo" can be animated, and the Wikipedia article for Leo the Lion sure seems to think so. As you mentioned, it can also be called an "intro" but I don't think there's a more technical term for it than that. The usage of "intro" is also pretty wide, as it can also refer to a musical or textual introduction.