I am not so sure it is a good thing that I was the "winner"... as you might have noted from the tone of my post, I feel the whole "_____ medium" thing is pretty played out. Adding "Medium" to your name was a bit of a fad about 6 - 7 years ago as a lot of design firms were moving into the internet space.
Have you done a trademark search yet? The reason why I immediately thought about a design firm is that there are several firms that already exist that have similar names. Rare Medium is one. MediumBold is another (although that is also a typographic reference).
It's a somewhat ambiguous play on Media... which is actually short for Medium.
Not short. Media, in the traditional art sense, is the pluralized version of medium.
However, in the context in which you are speaking it is probably more appropriate to think of "media" as content and "medium" as the channel through which you will communicate.
A strong brand and direct marketing should be able to overcome that.
I think your general worries are unfounded. As an advertising agency, you do not have to brand yourself to the public. You are not "competing" against McDonalds, etc.
Furthermore, I don't think you need to worry about people mixing up "media" and "medium". As someone who works within this field I see the above two words as fundamentally different elements. Any corporate communications manager who mixes up "media" and "medium" is one you don't want to work for anyway!
If I think back to the Ad agencies that I have worked with in the past, none of them were "publicly branded"... in fact, quite the opposite:
Crispin Porter + Bogusky
The Barbarian Group
TBWA\Chiat\Day
Mullen
Arnold
"Brand" yourself with good work instead. Get recognized within the community. The rest takes care of itself.
