Shamelessly lifted from a blog I read, and not yet credited because I wish to reduce the chances of peeping for answers.
Basically, your answer will look like: “Of course - Billy Thomas, the famous jazz player, and Thomas Billy, the CEO of Peoplesoft.”
Except there ain’t no such people as Billy Thomas or Thomas Billy, as far as I know.
But what pairs do fit this question?
Like this?
Harper Lee, author of To Kill a Mockingbird, and Lee Harper, English goalkeeper.
Bingo.
Actors David Keith & Keith David (although I’m not sure that either qualifies as “very famous” per the blog entry)
ETA: Looks like a winner was declared whilst I was posting
There’s not necessarily “a” winner; undoubtedly there are multiple pairs of names which fit.
If you stretch slightly the ‘moderately significant’ qualifier, and allow switching an ‘e’ and ‘a’, my stock answer is (training camp) teammates Ray Allen and the slightly less famous Allan Ray
Oh good lord, there’s an hour of my life I’ll never get back.
How about Ray Charles, musician and Charles Ray, Artist
Or David King, Scientist and King David, religious leader (OK, maybe King wasn’t his first name, but they would have called him King had people spoken English back then)
I must admit after thinking of these 2, I did search “people with first names for last names” Then picked some likely ones and looked up their counterpart.
[spoiler]
or Coleman Francis, director and Francis Coleman, director
Kelly George, beauty queen and George Kelly, major league first baseman
Journalist Lawrence Martin and comedian Martin Lawrence
General Lawrence Thomas and painter Thomas Lawrence
Outfielder Lloyd Christopher and actor Christopher Lloyd
Former United Technology CEO George David and British Prime Minister David George
Founding Father Luther Martin and Reformationist Martin Luther
Soccer player Marvin Lee and actor Lee Marvin
Hockey Player Scott Campbell and actor/voice talent Campbell Scott
Democrat Representative Scott Randolph and actor Randolph Scott
Singer Neil Simon and other singer Neil Simon
Thomas Henry, illustrator and actor Henry Thomas
John Collins, the canny Scottish playmaker, finished his football career with Fulham. The year he retired, Fulham signed the Liberian/Dutch player Collins John 
Judy Collins tells the store of introducing her brother Denver John to John Denver.
:dubious:
Palestinian activist Zoughbi Zoughbi and … himself.
whoops, the second one is obviously Simon Neil
Washington Irving and Irving Washington, cricketer.
Any number of William Kings, and any number of King Williams.
IN that case, Sirhan Sirhan.
And if you allow fictional characters, Catch-22’s Major Major Major Major and himself.