Is there a name for these kind of doubled words?
Note that some rhyme and others do not.
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hanky-panky is an example of rhyming reduplication
zig-zag is an example of ablaut reduplication
I believe the word you're looking for is reduplication.
Reduplication in linguistics is a morphological process in which the root or stem of a word (or part of it) or even the whole word is repeated exactly or with a slight change.
Wiktionary gives specific types:
- Exact type: acute-null accents; baby-talk-like
- bye-bye, choo-choo, night night, no-no, pee-pee, poo-poo, etc.
- Ablaut type: acute-grave accents, high-low vowels, front-back vowels.
- bric-a-brac, chit-chat, criss-cross, kitty-cat, knick-knack, jibber-jabber, splish-splash, zig-zag, sing-song, etc.
- Rhymed type: acute-acute accents, varied initials.
- claptrap, hokey-pokey, honey bunny, razzle-dazzle, slim jim, super-duper, teeny-weeny, wingding, etc.