Yes, there has been serious study of “secret languages” as they’re usually called. People who study children’s folklore (subcategory: folk speech) and linguists both study them, for different reasons. The classic place to start is Iona and Peter Opie’s The Lore and Language of Schoolchildren, which has a few pages, but I’d also recommend Simon Bronner’s American Children’s Folklore. The Opies list categories:
rhyming slang / crooks’ language [using phrases based on rhymed words to disguise speech]
back slang / Pig Latin [moving the inital sound to the end with added vowels]
pidgin English / double talk [inserting sounds within words]
I’m torn. You’re doing exactly what I do when I jump down people’s throats for using “myth” to mean “something untrue,” abusing the technical academic definition for their cheap and lazy vernacular thrills.
Children’s pidgins are known as such, and have been for over half a century. The Opies published their book in the 1950s. Nobody thinks they are the same thing as true pidgins, the sorts that linguists talk about, but at some point somebody must have made a connection, and the name sticks.
Children’s pidgin <does not equal> pidgin, but it’s still a perfectly appropriate term to use for the things the OP is talking about.
They are called ludlings and they are exceedingly common. Linguists love them because, despite being “children’s games”, they follow all kinds of formal rules on formation, insertion, etc. Bruce Bagemihl (University of British Columbia, 1988) wrote a dissertation on ludlings called Alternate phonologies and morphologies where he classified all ludlings into four broad categories - infixing/affixing, templatic, reversing, and replacement.
Finnish doesn’t have Pig Latin, we have “Pig German” (siansaksa). Another one we have is “kontinkieli”, which works as follows:
Take a sentence like “My name is Aura”= Minun nimeni on Aura.
Insert the word “kontti” in between each word. Minun kontti nimeni kontti on kontti Aura kontti.
Swap the first syllables of each word-kontti-pair. Konun mintti komeni nintti kon ontti koura antti.
There have been a lot of these kind of language games, some in use, some not so much. I found this website (in Finnish, sorry, but I only linked it for demonstratory purposes) which lists different “play languages”, and there’s over 40 listed.
When I was a teenager, we had a version of “bicycle,” where we inserted “eez” before every vowel sound. So “English” became “Eezengleezish.”
My friend and I used to speak this way in front of his mother, thinking that she couldn’t understand us. It was a long time before she inadvertently let us know that she understood us all along. She had spoken the same way when she was that age.
Australian Aboriginal languages (real ones, not novelty ones) often differ between the genders. It was apparently a source of no end of mirth when the early Englishmen picked up words from women and tried to talk to the men.