We are looking for a replacement for a fixture that attaches to our hand held shower and hose. It has a female connector that slides on top of the male connector as shown. Could someone tell us what this is called, or where we could purchase a replacement?
You were not very clear with your question.
I am assuming that you are looking for the fitting to which the sprayer head attaches, which then drops over the bracket peg in your first picture.
It is called a swivel connector. They are not "generic", they are specific to the manufacturer of your hand-held shower equipment. This one is from Alsons, a very common brand in the U.S.A. and the one I think you may have. Do an internet search for Alsons Swivel Connector.