The word you might be looking for is "earicon" (also sometimes known as an "earcon"), or the slightly less jargonic "audio icon".
You'd be hard-pressed to find this term documented in dictionaries or even online because it's mostly used as jargon within the advertising and audio/video production industries. Due to confidentiality agreements, I can't provide written materials to back this up, but I've worked in the audio branding business for eight years and every producer and designer I've met knows what an earicon is.
More formally speaking, there is a legal definition of a "service mark", which in the case of certain companies can consist of a unique sound and the spoken name of the company. This is used by many telephone service providers and other media-centric companies. Think of the "AT&T tone", which is followed by a female voice speaking the name of the company.
Finally, the broadest term that encompasses all representations of a company in media is "corporate identity."
After talking with a few colleagues and checking various sources, here are some more candidates:
- auditory sign-off
- donut (a kind of ad that has music and pre-recorded audio at the beginning and end)
- jingle (originally referred to the musical logo of a company or brand)
- bed (the music over which the company name/brand is read)
- talk over (the spoken words played over the "bed")
- sonic branding
- sonic logo
- brand song