Lady...? Lady J... ? Lady Jaye!

In Lady Jaye's first initial appearance in G.I. Joe: A Real American Hero #32 (1985), her codename was originally spelled "Lady J."  

This is actually her final major debut appearance.  Lady Jaye was created for and first introduced in the Sunbow cartoon, where she played a prominent role in The Revenge of Cobra five-part mini-series.  After that, she was released as an action figure and eventually made her debut in the comic series shown below.

The issue saw "Lady J" and Ripcord arrive as replacements for Grunt and Scarlett.   Lady Jaye seemed disrespectful towards Scarlett, but this wasn't developed into a full-blown feud.  

With "Lady J,"  the letter J could represent/be taken as Joe, making her code name literally Lady Joe, or the female Joe, woman Joe, lady Joe, what have you.  Or the other possible option would be Jane, making her the G.I. Joe's Lady Jane or G.I. Jane. 

This character appeared to be ideally suited to serve as the female mascot for G.I. Joe:  A Real American Hero IP, similar to how Grunt represented the male mascot, as he is the visual featured in the upper corner of the comic book.  

Grunt felt generically like a male soldier, and so did "Lady J" as a female solider.

When people think of the female members of G.I. Joe, Lady Jaye is often likely the first character that comes to mind, thanks to her starring role in Sunbow animation (Scarlett likely is said for people who were big into the comics, but the cartoon reached far more people).

The transition from "Lady J" to Lady Jaye was believed to be a phonetic spelling change.

This shift was to give Lady Jaye a more distinct and complete codename.  

The name "Lady J" felt too terse, utilitarian, and abrupt. In contrast, Lady Jaye adds a sense of mystique, a bit of elegance, reflecting the character's theatrical finesse as a covert specialist.

Lady J?  No!  Lady Jaye!

Lady Jaye was the prominent woman on the G.I. Joe team, the female archetype within what was primarily a toy line marketed to boys.