“A guy walks into a bar…”  is a typical form of what has been called the “bar joke.” A screwdriver version is:
   
“A screwdriver walks into a bar. The bartender says, ‘Hey, we’ve got a drink named after you.’ The screwdriver says, ‘You’ve got a drink named Philip?’”
 
A screwdriver is a cocktail, but a Phillips screwdriver is a tool. Philip/Phillip is also a personal name. The classic version of this type of joke involves a grasshopper and a grasshopper cocktail: “A grasshopper goes into a bar and orders a martini. The bartender says, in passing, ‘Do you know we have a drink named after you?’ The grasshopper says, ‘No really? You have a drink named Howard?’”
 
The joke also works with other names, like the grasshopper version. The screwdriver joke with the name Bob was posted on the newsgroup alt.philosophy on June 26, 2000. The screwdriver joke with the name Murray was posted on Twitter by Sheila Dennis on April 21, 2010. A Philip version was posted on Twitter by Super City on July 12, 2013. A Phillip version was posted on Twitter by Mike Topp on July 20, 2013.
   
     
Google Groups: alt.philosophy
Immortality
Weasel
Jun 26, 2000, 3:00:00 AM
(...)
That’s funny. I have one for you: A 6 foot tall screwdriver walks into a bar. The bartender looks over at him and says “Hey, isn’t that funny—we have a drink named after you.” The screwdriver replies, incredulously, “You have a drink named Bob?” Har har har.
       
Twitter
Daniel Friedman
@danloufried
just did stand up for the first time tonight… a screwdriver walks into a bar!
12:55 AM · Jan 21, 2010
   
Twitter
Sheila Dennis
@SheilaDennis
A screwdriver walks into a bar. Bartender: “Hey, we have a drink named after you!”
The Screwdriver: “You have a drink named Murray?”
10:05 PM · Apr 21, 2010
   
Twitter
Chuck Gose
@chuckgose
@jlisak A screwdriver walks into a bar. The bartender says, “Hey, we have a drink named after you!”
3:31 PM · Apr 23, 2010
     
Twitter
Bart Millard
@BartMillard
A screwdriver walks into a bar. Bartender says “hey we gotta drink named after you.” Screwdriver says “you gotta drink named Ted?”
Ha ha ha
1:46 AM · Jun 19, 2010
   
Twitter
dan0vision
@dathomso
A screwdriver walks into a bar. Bartender says “hey we gotta drink named after you.” Screwdriver says “you gotta drink named Ted?”
9:42 AM · Jun 19, 2010
   
Twitter
Disco Cigarettes
@DiscoCigs
A screwdriver walks into a bar The bartender says, “Hey, we hve a drink named after u!” The Screwdriver says, “U have a drink named Murray?”
10:40 AM · Sep 9, 2010
   
Twitter
Stefan Hawes
@hawes
A screwdriver walks into a bar. Bartender says “Hey, we’ve got a drink named after you.” Screwdriver says “You’ve got a drink called Steve?”
11:23 AM · Mar 2, 2011
 
Google Books
More One Liners, Jokes and Gags
Compiled by Grant Tucker
London, UK: Biteback Publishing
2013
Pg. ?;
A screwdriver walks into a bar. The bartenders says, ‘Hey, we have a drink named after you!’ The screwdriver responds, ‘You have a drink named Murray?’
 
Twitter
Super City
@supercitytv
A screwdriver walks into a bar and the bartender says “we’ve got a cocktail named after you!” The screwdriver replies “what, Philip?” #LOL
5:10 AM · Jul 12, 2013
     
Twitter 
Mike Topp
@MikeTopp
A screwdriver walks into a bar. The bartender says Hey we have a drink named after you. The screwdriver says You have a drink named Phillip?
9:41 AM · Jul 20, 2013
   
Twitter
The Park Bench
@ParkBench2014
A screwdriver walks into a bar. The barman says, “We have a drink named after you!”
The Screwdriver says, “You have a drink called Phillip?”
11:51 AM · May 13, 2014
 
Reddit—Dadjokes
Posted by u/[deleted] January 28, 2015
A screwdriver walks into a bar…
The bartender looks up and says “Hey, we’ve got a drink named after you.”
The screwdriver replies, “Really, you’ve got a drink named Harold?”
   
Reddit—Jokes
Posted by u/B936 July 4, 2015
Screwdriver walks into a bar
Bartender says hey man we have a drink named after you?
The screwdriver asks “you have a drink named Steve?”
 
Reddit—Dadjokes 
Posted by u/Anthokne July 29, 2015
A screwdriver walks into a bar…
The bartender looks over at him and says ” Hey, I’ve got a drink named after you!” Confused, the screwdriver looks to the bartender and replies, “You’ve got a drink named Harold?”
   
Reddit—Jokes
Posted by u/TheMadHatterOnTea December 10, 2015
A screwdriver walks into a bar…
The bartender sees it and shouts out, “Hey! We have a drink named after you!”
The screwdriver gets excited and says, “You have a drink named Larry?
 
Reddit—Jokes
Posted by u/jaysunn72 September 30, 2016
A screwdriver walks into a bar. The bartender says, “Hey, we have a drink named after you!”
The Screwdriver responds, “You have a drink named Murray?”
         
Twitter
JN ~
@llamesjj
>A screwdriver walks into a bar.
>The bartender exclaims “Hey we make a drink named after you!”
>The screwdriver responds, “what, Philip?”
4:20 AM · Oct 20, 2016
 
Reddit—Jokes
Posted by u/CosmicNoire January 21, 2017
A screwdriver walks into a bar…
The Bartender says, “Hey! We have a drink named after you!”
The Screwdriver says, “You have a drink named Murray?”
 
Reddit—OutlandishAlcoholics
Posted by u/imyselfamwar March 3, 2017
A screwdriver walks into a bar….
Bartender says, “Hey pal. Welcome. We even have a drink named after you!”
Screwdrivers says, “You have a drink named ‘Joseph’?”
       
Twitter
Mike Topp
@MikeTopp
A screwdriver walks into a bar. The bartender says hey we have a drink named after you. The screwdriver says you have a drink named Philip?
7:30 PM · Jun 18, 2017
 
Reddit—Dadjokes   
Posted by u/[deleted] July 11, 2017
A screwdriver walks into a bar…
Bartender says “Hey you know we got a drink named after you? Screwdriver says “You got a drink named Bob?!”
   
Twitter
Queef Whisperer🍺Twi
@Despicable_Ang
A screwdriver walks into a bar…. The bartender says, “Hey, we have a drink named after you!”
The screwdriver replies, “You have a drink named Philip?
#IllBeHereAllWeek #TipYourWaitresses
3:47 PM · Apr 6, 2018
 
Reddit—Jokes
Posted by u/Goku_Kakarot91 January 4, 2019
A screwdriver walks into a bar..
bartender says, we have a drink named after you, to which the screwdriver responds “you have a drink named eric?”
   
Redit—Dadjokes
Posted by u/whattajosh April 1, 2019
A screwdriver walks into a bar. The bartender says “hey, we have a drink named after you!”
The screwdriver replies “what? Kevin?”
       
Reddit—GrandBLue
Posted by u/DrThots July 5, 2020
Screwdriver joke explained?
I don’t understand the screwdriver joke at the bar scene, can someone please explain?
COMMENTS
aspirat2110
There is a cocktail named “Screwdriver”, but they just put in a literal screwdriver.
https://en.wikipedia.org/wiki/Screwdriver_(cocktail)
 
Reddit—Jokes
Posted by u/AboveReason August 30, 2021
A screwdriver Walks into a bar and takes a seat in front of the bartender.
Bartender notices and heads his way over then says “hey bud, we’ve got a drink named after you so here’s one on the house”
Confused, the screwdriver asks “wait, you have a drink named Steve?”
 
Reddit—Jokes
Posted by u/Dethjonny July 19, 2023
A screwdriver walks into a bar
The bartender says! “Hey, we’ve got a drink named after you.”
The screwdriver says, “You’ve got a drink named Philip?”