I think the song that starts “Chestnuts Roasting on an Open Fire” was first just called “The Christmas Song.” Not sure if inertia has changed what it is typically called these days.
The pop song that starts “How gentle is the rain” to the classical minuet tune (you may recall it from Mr. Holland’s Opus) is properly titled “A Lover’s Concerto.” I’m not sure what people typically call it, but the title is not intuitive from the lyrics, as it never appears.
Scott Joplin’s “The Entertainer” is frequently called, mostly by people of my parents’ generation, “The Sting”.
I’ve never been a big Zeppelin fan, and hence own none of their records. Consequently, I’ve heard the titleD’yer Mak’er hundreds of times, but never connected it to the song you’ve quoted, which I’ve also heard hundreds of times.
The Wang Chung song best known as “Everybody Wang Chung Tonight” or just “Everybody Wang Chung” is really “Everybody Have Fun.”
The “theme from 2001” is “Thus Spake Zarathustra,” or in the original Klingon, “Also Sprach Zarathustra.”
Big Country’s biggest hit is “In A Big Country.” I won’t forget that since I once lost a trivia game in which I claimed the song as an example of “80s hits titled the same as the band that sang them.”
Nazareth’s Hair of the Dog, which I hear often refered to as some form of “Now your messin’ (with a son of a bitch)”. Probably because the title is not said in the lyrics.