What is the symbolism of using American Psycho protagonist's name in Dexter?

I think this is just a simple thing thrown in from the director/writer to try to draw a comparison of Dexter to Bateman. Both are killers but when thought about, Bateman is more vain and reckless than Dexter, the chainsaw scene is my reference here. Whereas Dexter is quiet, methodical, and adheres to a strict code whenever he can.

In a relative sense, one can almost say Dexter is the kinder killer as he actually begins to care about the people around him and defend them where Bateman is truly just a psycho, and would probably end up on Dexter's table, had he ever gotten word of him.

This is obvious!

It's a joke. Dexter doesn't watch many movies and doesn't have any idea about American Psycho. His ignorance of modern-culture and in particular movie characters is stressed in a previous episode when he doesn't recognise his girlfriend's costume as being Lara Croft. He thought the alias would make him appear innocent (he even says this in the scene), but the joke is that if any of them saw that name whilst investigating the case, they would instantly put 2 and 2 together.

Absolutely loved how they approached this.

No, Bateman and Dexter both introduce an element of existentialism into the mind of the psychopath; The subtle insertion of what it means to cope with your existence while being in the world and trying to seem, "Normal".

Both characters exhibited existential angst with their decisions which we interpret as an emotionless process, however, the very process of investigating their actions ties them to the world as a sort of purpose in a purposeless world.