I sort of get what you mean. I had just assumed that JustEat got renamed Menulog when I saw some stuff online with the same logo but then I never really cared much about JustEat either, just a service that does a thing. Certainly making a ‘log = poo’ connection is a bit odd.
However, that ‘replace the word in the jingle’ thing is common I reckon. There was a Cadbury’s Heroes advert maybe 8 years back that was in the UK that has a song where the whole point was that it rhymed ‘heroes’ with something. But in Aus they’re called ‘Favourites’ so they had the same song but they’d changed heroes to favourites meaning it just sounded absolutely fucked due to the obvious rhyme being missed. But I guess you’d not know unless you knew.