I would be a little careful with implementing a function like this because i think it can be hard to really make it work in a good way for the users.
What f.example with customers having branch offices where only the address is different?
And be careful so you do not break any logic that might be used later for creating customers from other sources than manual input.
In the standard system there is a merge function that can be used to merge customers if you for some reason got a doublet.

In my experience it is better to create a page that can show go to from time to time that can show you potential doublets and then you can check if they actually are doublets or not.
I know many users wish for functions like this when they are new to a system, but then after a while they really don't see a need for it any more.
But Josh have given you a good approach if you really want to go ahead with it.