(I also dislike a cluttered desktop. In fact, I do not use desktop icons at all.)
There are a number of ways to track it down.
Open a terminal and try starting it with the command komodo.
If that doesn't work, you can try the whereis command. See man whereis for details. There is also the locate command (see man locate) but it will likely return more information than you need.
It is likely in the /usr/bin directory. Another way is to try the command ls /usr/bin/komod*. That should turn it up if the name of the program is not just komodo, but is actually something like komodo-1.7.
Once you know where it is, you can add it to a menu or just start it from the command line.