Well this has probably happened before, but it is going to be amplified when it is a high-profile church like Mark Driscoll's Mars Hill (TM):
We’re not the only church called Mars Hill, and occasionally there arises confusion between us and other churches that share the “Mars Hill” name, particularly as we now have our churches in four states. This was the case recently when one of our members called us to find out if we had planted Mars Hill churches in the Sacramento, California area. We had not, but when we went to these churches’ websites, it was obvious to us how people could be confused. Each of these three connected churches in the Sacramento region—planted in 2006, 2007, and 2010—bore the “Mars Hill” name and their logo was substantially similar to the logo we’ve used since 1996.
When cases like this arise in the business world, it’s customary for a law office to send a notice asking the other organization to adjust their branding to differentiate it. This is commonly referred to as a cease and desist letter. On September 27, 2011, our legal counsel sent such a letter to these three Mars Hill churches requesting that they change their logo and name. In hindsight, we realize now that the way we went about raising our concerns, while acceptable in the business world, is not the way we should deal with fellow Christians. On Friday we spoke with the pastor of Mars Hill in Sacramento to apologize for the way we went about this.
There is more to the post at the above link. Traditional denominations have hundreds of namespace collisions, since most churches are named for saints, or have other predictable names (e.g. "First Baptist Church", or "Holy Trinity"). As a commenter on another blog points out, this seems to be the result of the "multi-site" era, where the same name is supposed to represent the same institution in all locations. I wonder if the Vineyard or Calvary Chapel movements ever ran into this problem.
Oddly enough, there is already another high-profile "Mars Hill" church in Michigan (run by Rob Bell). May the church with the best lawyers win!