Make Me Smile by Chicago - it was practically an anthem back in the day for some of us. What good times, looking back now, our futures were so bright.
But that’s what I mean. I’ve never even heard casual listeners name that as a Santana song. It just seems so odd to me. If they could name one, it’d be either one of the modern songs (like “Smooth”) or maybe “Black Magic Woman.”
Word. Are we listing things that some people who may not even exist think? OK let’s go! Stairway to Heaven is the only song I know by the Clash.
Murray Head. 16 albums, but who knows any song of his but Superstar and One Night in Bangkok?
Funnily enough, the only song I know by them is “Particle Man”, because my friends and I from way back used to get high and play that song repeatedly and we never could get the order of who fights who and wins correct.
Perfect Strangers
What about *The Outlaws *with “Green Grass and High Tides Forever”?
Yeah, okay, I get the joke, but not as a real occurrence.
To those I’ll add Love to Love You Baby, her first big song.
I agree with that but you’re fine-tuning the OP.
How about Steppenwolf, then? With “Magic Carpet Ride” and “Born to Be Wild,” that’s two, so there are better examples, but they recorded almost 20 albums. This has always been my favorite:
The Wiki entry for B.B. King indicates 45 albums, and I think most people can only name “The Thrill is Gone.”
Even more unfair, Kurt Weill and Bertolt Brecht did many great things but are mostly known for “Mack The Knife”. 
Back to bands, how about the Bonzo Dog Band, which had one “hit” (Urban Spaceman) and is probably most recognized for The Intro And The Outro, but had lots of great songs, including my personal favorite, Humanoid Boogie:
Well, the Humanoid Boogie’s got the humanoid hip-types
Jumpin’ and-a jivin’
Burnin’ out their energy cells like an infrared hot dog
Motorbike heart beats flutter to the stutter
Of the humanoid heart-throb sobbin’ out a ticker tape tune
By the light of the moon
Bleep, bleep, keep rockin’, daddy, do the stroll
Because the Humanoid Boogie’s full of humanoid rock and roll
Los del Río formed in 1962 and released 30+ albums up to 2012
Iron Butterfly. 9 albums, still around, known for “Innagadadavida” or however you spell it.
While I am no fan of theirs I can name (and hum the chorus) of two A-Ha songs. The inevitable Take On Me but, in the UK, The Sun Always Shines On TV was also a big hit.
As for Dexys Midnight Runners I can name (and hum) Eileen but also the earlier hit Geno plus The Celtic Soul Brothers plus I remember their cover version of Jackie Wilson Said… Or - for UK viewers of Top of the Pops - Jocky Wilson Said
TCMF-2L
Well congratulations on living in such musically knowledgeable areas. Most of the 20-25 year olds I work with have never even heard of War.
My kids know War! And Sly and the Family Stone, and James Brown, and Parliament / Funkadelic, and Aretha, Etta James and Billie Holiday. How can I claim to be a music geek here if I’m not one at home? 
They get mad at me if I play too much metal, or if the Jazz I put on is too far out, or if I put on harpsichord Bach vs piano Bach - too tinny for them.
This might be the thread winner.
Oh, is it meant as a joke? Then I was being whooshed, which would not be the first time. I took the tone as relating an actual experience. (And, serendipitously enough, today at the amusement park with the kids, “Black Magic Woman” was playing over the PA.)
Don’t you have to have a well known song to be the winner?