Elliott C. answered 10/08/19
Proficient Hebrew Speaker with 8+ Years of Experience
Your question seems rather specific, and I can't think of any particular "hide-and-seek" type rhymes if that's what you're asking. However, there is a very useful rhyme that I learned and Israeli elementary school children typically learn in order to memorize pronouns (and a few other words):
מי is who, הוא is he, היא is she, אני is me, and דג is fish ;)