I feel that 'secret handshake' isn't an appropriate name for the way some people elaborately greet each other. Some friends have complex hand grasps and what not, and other people may simply shake hands and pat each other's back.
This is called a dap greeting:
At its most basic, a dap greeting is simply a ritualized handshake, but it usually includes a series of gestures, with the gestures being performed in a specific and choreographed order. Many people learn dap greetings very young, by watching and interacting with other people in their communities, and often such greetings are exchanged almost reflexively, much like businessmen shake hands when meeting each other. A dap greeting can include snapping, wiggling fingers, slapping hands, and other forms of contact, and it can last anywhere from a few seconds to 20 minutes.
Maybe something involving greeting would be more appropriate. For example,
Jack and Jill developed their own greeting to use with each other.
That being said, "secret handshake" usually refers to a special and secret way for members of a group to greet each other. For example, under conspiracy Merriam-Webster writes the phrase:
members of the conspiracy recognized each other by a secret handshake