By golly, you’re dead-on there.
Boobs. The answer is boobs. Sweet dreams are made of boobs.
(Or so my then teenage brain interpreted the song)
What did The Eagles and The Eurythmics have in common?
Both insisted that there was no “the” in their name.
Nah, it is clearly ‘Bees’, which is what I sing when it comes up in rotation. 
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I always thought it was “thee’s” as she was singing to all her ex-lovers.
Same for the duo comprised of Karen & Richard.
Well, that makes no sense. They actually were “The” Carpenters, since it’s their name. Going by “Carpenters” implies that they’re woodworkers.
But, does The The have a The in the name, or not?
Smashing Pumpkins as well. First album. Third album. Then back to seventh album. And changed mind again with ninth album.
According to link, Annie covered this in her book:
“After much thought, we decided to name the act ‘Carpenters’ (No ‘The’; we thought it sounded hipper without it, like Buffalo Springfield or Jefferson Airplane.)” - Richard
Talking Heads got so irritated with people calling them The Talking Heads, they actually put out an album titled, The Name of This Band is Talking Heads, just to drive the point home.
The Pink Floyd only released one single.
The Electric Light Orchestra released two albums and then changed their name to Electric Light Orchestra.
One of the harder bands to google.
Hall and Oates actually prefer to be called Daryl Hall and John Oates, but I don’t see that happening anytime soon.
Except that’s not the rhyme scheme in the lyrics. “Disagree” almost-rhymes with “seven seas”, and it’s not supposed to rhyme with “this”. The rhyme scheme is ABCBD in the chorus.