In DS2, convergence was the necromorphs coming together to reform the Hive Mind. I had this idea where the Nicole illusion was actually the Hive Mind from the 1st DS, barely alive through a psychic synapse implanted in Isaac's mind and taking the form of his dead girlfriend. I thought of this when in the final battle, illusion Nicole said "yours is the last body we need to be reborn" to Isaac.
Where did you get the Idea that convergence was to create a new Hivemind?
As far as the books and games goes, there is no explanation of what convergence is, only theories.
Just thought it up :p But it's like you said, only theories. I looked at the wiki just now though, and it says Convergence is when the markers starts to gather nearly every necromorphs in the vicinity and merges all of them to form super large, moon sized necromorphs