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.
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This is called a dap greeting:
Maybe something involving greeting would be more appropriate. For example,
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: