I watched Farscape fairly religiously back when it was first aired on the BBC. I've caught some episodes recently sitting up with my teething Son, and found myself asking ...
At what point did John start calling his gun Winona, and why?
In A Clockwork Nebari (S02E18)
The name actually came from Ben Browder, and is a reference to Winona Ryder. I've heard both that it's because another cast member of that episode reminded him of Johnny Depp, and because of Ryder's role in Alien: Resurrection. I don't know if either/both are true.
I've also seen a quote from Browder that all guns should be named after beautiful women. I don't know if he's named any others in other shows, though.
In-universe, it just seems like the sort of thing that Crichton would do - a reference to an Earth actress, naming a weapon - those all fit the character. I don't think there's any in-universe explanation for Winona specifically, other than she's female and famous.
The first time John refers to his beloved pulse pistol as Winona is at the beginning of "Clockwork Nebari" towards the end of season 2. The male Nebari character in that episode reminded Ben of Johnny Deps famous Edward Scissor Hands, I guess that put winona on his mind!
Crichton: [finds a pulse pistol] What do we have here? A pulse pistol. What are you doing here on your own? You're going to come in handy. You need a name... Winona. I'm gonna call you Winona.
There's no indication why he chose this particular name.
Out of universe, Ben Browder personally chose the name of his character's gun, naming it after actress Winona Ryder
Q. Who or what is the antecedent for John naming his pulse pistol "Wynonna"? ... (And do we finally have the spelling right? )
BB: Winona Ryder. I continue to screw up the spelling of that one. All important inanimate objects should be named after beautiful women. My biggest regret is that I never seized upon the opportunity to name the Farscape module... But in my soul, I call her "Betty".
The first instance I can recall him using that name is in "Green Eyed Monster" S3E8.