“‘I have a split personality’ said Tom being Frank” is a joke that was posted on the website Pun of the Day in 1999. “Frank” is a name and “frank” is also a word meaning directly or honestly. The joke is an example of a “wellerism” or “Tom Swifty.”
   
“‘The doctors say I have a multiple personality disorder,’ said Tom, being frank” was posted on the newsgroup Google Groups: alt.humor.puns on April 7, 2004. “‘I’m schizoid,’ said Tom, being frank” was printed in the BMJ (British Medical Journal) on July 17, 2008. “‘I have multiple personalities!’ Said Bill, being frank” was posted on Twitter by aspen on May 30, 2011. 
   
             
Wikipedia: Wellerism
Wellerisms, named after sayings of Sam Weller in Charles Dickens’s novel The Pickwick Papers, make fun of established clichés and proverbs by showing that they are wrong in certain situations, often when taken literally. In this sense, wellerisms that include proverbs are a type of anti-proverb. Typically a wellerism consists of three parts: a proverb or saying, a speaker, and an often humorously literal explanation.
 
Wikipedia: Tom Swifty  
A Tom Swifty (or Tom Swiftie) is a phrase in which a quoted sentence is linked by a pun to the manner in which it is attributed. Tom Swifties may be considered a type of wellerism. The standard syntax is for the quoted sentence to be first, followed by the description of the act of speaking. The hypothetical speaker is usually, by convention, called “Tom” (or “he” or “she”).
 
Pun of the Day   
Great One Liners of the Month - November 1999
(...)
4. ‘I have a split personality’ said Tom being Frank.
 
Google Groups: alt.humor.puns
Puns of the Weak 10-29-99
Stan Kegel
10/31/99
(...)
“I have a split personality,” said Tom, being Frank (Pun of the Day)
   
Google Groups: rec.humor.jewish
Puns of the Weak: 4-21-00
Stan Kegel
4/22/00
(...)
“I have a split personality,” said Tom, being frank. (Paul Benoit)
 
Google Groups: alt.humor.puns
Specialty Puns of the Weak 04-07-04
Stan Kegel
4/7/04
(...)
“The doctors say I have a multiple personality disorder,” said Tom, being frank. (Stan Kegel)
 
Google Groups: alt.humor.puns
Specialty Puns of the Weak 01-12-05
Stan Kegel
1/12/05
(...)
“The doctors say I have a multiple personality disorder,” said Tom, being frank. (Stan Kegel)
   
Google Books
Jumpstart! Creativity:
Games and Activities for Ages 7–14
By Steve Bowkett  
New York, NY: Routledge
2007
Pg. ?:
‘I must have a split personality,’ said Tom, being frank (my personal favourite).
 
17 July 2008, BMJ (British Medical Journal), “Tom Swifties” by Jeff Aronson, pg. 836:
3. Adjectival Swifties
(...)
“I’m schizoid,” said Tom, being frank.
   
Twitter
WordPlay
@wordlaugh
“I have a split personality,” said Tom, being frank.
6:48 PM · May 1, 2009·Twitter Web Client
   
Twitter
Gherkin 🥒
@TheLastGherkin
“I think I have multiple personality disorder,” said Tom, being frank.
5:55 AM · Jan 2, 2010·Twitter Web Client
 
Twitter
aspen
@kiss_my_asspen
“I have multiple personalities!” Said Bill, being frank(:
12:53 PM · May 30, 2011·Twitter SMS
   
Twitter
Sam Leitermann-Long
@samleitermann
“I think I have multiple personalities,” said Steve, being frank. #epicpun
5:32 PM · Jul 6, 2011·Twitter SMS
   
Twitter
Dr. Jeff C. Ho
@JeffCFHo
Heard a great joke the other day: “I think I have multiple personalities,” said Tom, being frank.
2:16 PM · Jul 8, 2011·Twitter Web Client
   
24 August 2011, Creators Syndicate (Los Angeles, CA), “Bright Lights, Big CT” by Scott LaFee:
BEST MEDICINE
“I have a split personality,” said Tom, being Frank.
 
Twitter
Andrew (Toycat)
@ibxtoycat
“i think i have multiple personalities,” said Steve, being frank.
2:51 PM · Nov 23, 2016·TweetDeck
     
Reddit—Dadjokes
Posted by u/Radish00 November 4, 2019
“I have a split personality,” said Tom, being frank.
 
Reddit—Oneliners
Posted by u/DoorHalfwayShut November 29, 2019
“I have multiple personalities,” said Carl, being frank.