I have a dataset that lists entities per district - where district is a named shape that exists on a map. I have a different dataset that contains entities of the same type, only instead of being positioned categorically (i.e. by district name) they are positioned using lat-long coordinates.

So, given a shape-file (in either ESRI or GML3), how can I transform a list of lat-long coordinates into a matching list of named districts?

I am looking for the most generic algorithm possible, but if there are tools/modules out there that perform this function natively, that would be good to know too.