There is no proper explanation as to why the Marsh Badge was called the Marsh Badge. There are many assumptions as to why this has happened.
To add even more suspense, the funny thing is that Koga/Janine the Poison-type Gym Leader, gives out the Soul Badge. Something one would think would relate to psychic ability - soul. Many think it was an error in programming, or a typical translation error. However, this assumption might be wrong!
This only supports this controversy a little - the Japanese translation for the badges were Gold Badge (Marsh) and Pink Badge (Soul). Of course, it doesn't really support the theory at all, but it gives some distinction. A soul could be referred to as pink, and a marsh could be referred to as gold (or, dark yellow anyway). It makes sense in a way though. There is no real understanding as to why this exists. Many think it was an error in translation, and I'm with this all the way.
So, there is no real reason as to why this is.
Hope I helped. (Probably didn't, but... yeah xD)