I am wondering if there is a standard for the placement of GFI outlets in the backsplash for a double vanity?
This is my first time, so I apologize in advance if this is redundant question! I've searched online and can't seem to find the answer.

It may change from place to place. You would have to check out the building codes for your township. They can sometimes be viewed online on your township's website. I believe, in my neck of the woods, that a GFI needs to be installed if it is within 6 feet of a water source.

You say vanity, which implies bathroom. All receptacles in bathrooms must be GFI protected. If your question is where it is to be placed, code does not address. It does require at least one outlet on a 20 Amp circuit that serves only that or another bathroom.

Good advice, not a standard but rather a building code. Varies only slightly from place to place since most towns follow an international code.

I believe, in my neck of the woods, that a GFI needs to be installed if it is within 6 feet of a water source.Possible, but according to the NEC a "water source" has NO bearing on GFI requirements.

I am wondering if there is a standard for the placement of GFI outlets in the backsplash for a double vanity?Yes, the NEC does address this. A receptacle must be placed within 36" of the outside edge of a basin.
So a receptacle placed in the middle of a double basin vanity would meet code. One receptacle to the side of one basin would not. You would need one on the side of each basin.