There’s a classic thread here about someone learning the difference between Jerry Lewis and Jerry Lee Lewis, but I couldn’t find it. 
I was made aware of another such name this week. I was discussing things with a Red Cross nurse this week, and she said that she liked Bernard Shaw. I told her I did, too. She seemed very surprised. It turns out that I was thinking of George Bernard Shaw, the famous plarwright, responsible for saint Joan, Pygmalion, and others too numerous to mention. (He didn’t like the “George” part, although he often initialed things “GBS”. Th Penguin editions leave the “George” out of his name on the covers).
But it turns out that she meant a black motivational speaker, who hasdreadlocks. I’ve never heard of him – unless it’s ex-CNN anchor Bernard Shaw with a different hairstyle. (A quick search of the internet shows that he is available as a speaker, but his photo has no dreadlocks. And it’s not his style).
so there’s another threefer for you.
And then there’s the Jim Morrison who played Bill Buchanan on 24.
The US president was James A. Garfield, but he was only prez briefly, so understandable error.
There are others. I think one used to be a recurring guest on the NewsHour, but I forget for whom he worked.
Al Kooper writes that people mistook him for Alice Cooper.
Back during the Beijing Olympics, there were a bunch of news articles about Michael Phelps’ father having divorced from his wife and not attending the Games.
The father’s first name? Fred.
Robin Williams, actor and comedian.
Robbie Williams,singer.
Robert Parker, author of the “Spenser” mystery novels
Robert Parker, noted wine expert
Robert Palmer, music writer.
Robert Palmer, writer of music.
Similarly,
Paul Williams, music writer, and
Paul Williams, writer of music
…plus the one from the Temptations, the British prog-rock singer, and the boxer.
From 1985 to 1990 there were two important Roger Craigs in pro sports in San Francisco. One was manager of the Giants, and the other was the star running back for the 49ers.
There are two musical John Williams - one is the composer/conductor who wrote a lot of movie scores and led the Boston Pops, and the other is a classical guitarist
I bet if we search we can find a pair named Robert Paul and Palmer Williams. 
Not to mention that guy with the locker.
There was also a Jim Morrison who played for the Pittsburgh Pirates in the 80’s, I think.
Tony Martin, British rock/metal vocalist (ex-Black Sabbath)
Tony Martin, German cyclist, competing in the Tour de France 2009
Also Tony Martin, farmer and vigilante, much admired by the British gutter press.
Ted Heath, bandleader
Ted Heath, prime minister
Luke Kelly, American football player
Luke Kelly, Irish soccer player
Luke Kelly, Irish singer, most powerful male voice in folk music; made gingervitis sexy.
D’oh! :smack: Maybe I was thinking of Garfield the cat?
And of course, Muhammed Ali the boxer changed his name to Muhammed Ali, so one assumes he probably knew about the ruler of Egypt. His birth name was Cassius Marcellus Clay, Jr., who was named after his father, Cassius Marcellus Clay, Sr., who was himself named after the “Lion of White Hall”, the American abolitionist, ambassador, and founder of the Republican party, Cassius Marcellus Clay.