An oronym is a pair of phrases which share a similar relationship as the homophonic

Homophone

A homophone is a word that is pronounced the same as another word but differs in meaning. The words may be spelled the same, such as rose and rose , or differently, such as carat, caret, and carrot, or to, two, and too. Homophones that are spelled the same are also both homographs and homonyms...

, in that they differ in meaning and spelling, yet share a similar pronunciation.. The words share a similar chain of consonant and vowel sounds, however they Examples include 'an ice cream' and 'a nice cream'; 'mint spy' and 'mince pie'; 'ice cream' and 'I scream'; 'stuffy nose' and 'stuff he knows'.

This particular '-onym

-onym

The suffix onym, in English and other languages, means "word, name," and words ending in onym refer to a specified kind of name or word, most of which are classical compounds. For example, an acronym is a word formed from the initial letter or letters of each of the successive parts or major parts...

' was invented by Gyles Brandreth

Gyles Brandreth

Gyles Daubeney Brandreth is a British writer, broadcaster and former Conservative Member of Parliament and junior minister.-Early life:...

 and first published in his book The Joy of Lex (1980). This term also featured in the BBC

BBC

The British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...

 programme Never Mind the Full Stops, which also featured Brandreth as a guest.

American comedian Jeff Foxworthy

Jeff Foxworthy

Jeffrey Marshall "Jeff" Foxworthy is an American comedian, television and radio personality and author. He is a member of the Blue Collar Comedy Tour, a comedy troupe which also comprises Larry the Cable Guy, Bill Engvall and Ron White. Known for his "you might be a redneck" one-liners, Foxworthy...

 frequently uses oronyms in his Appalachian routine. Notable examples include, "Initiate: My wife ate two sandwiches, initiate (and then she ate) a bag o' tater chips." and "Mayonnaise: Mayonnaise (Man, there is) a lot of people here tonight."

Mad Gab

MAD GAB

Mad Gab is a game created by Terry White in which there are at least two teams and 2-12 players. Each team has two minutes to sound out three puzzles. The puzzles, also known as mondegreens, contain small words that, when put together, make a word or phrase...

is a team oronym solving game.

Please note a totally different meaning in other language, whereas the oronymXXX has a topological meaning.