I have two theories on why Vodka has a codename and yet seems so lame.
1. This is another one of those literary devices and elements that Gosho has thrown in the DC franchise. My theory is that Gosho thought it was fitting to have the two original "bad guys" of DC be opposites. As we all know, in literature, opposites either attract or repel. In this case, they attract. Gin is tall, on the skinny side, has long hair, and is cunning. Vodka is a little shorter, on the fat side, has extremely short hair, and is mentally dull. Gosho probably just wanted to make it a harmless effect of "opposite bad guys". If you look carefully at many other series and movies and books with two main evil antagonists, you'll find that they usually contrast each other.
2. My other theory is that Vodka probably saved Gin's skin at one time or another. I'm betting on this scenario: The two happened to be working together on some project, and they got into a tight situation. Vodka might have either risk his life or sent one lucky bullet into someone saving Gin in the nick of time. The Organization was so grateful for still having a member like Gin alive and promoted Vodka up to his current status. Gin, equally as grateful for still being alive, continued to partner up with Vodka on future missions and became fond of the dull minded man.
If anyone has anything to add, please feel free.