"James" - "Jim", "Timothy" - "Tim", "Jim Possible" - "Impossible", "Tim Possible" - "Impossible" phonetic pun, with the Jim / Tim sobriquets. It is surmised by some his wife (mother of Kim Possible), or Dr. "Mom Possible," may be named "Sim Possible," derived from the root Simone, since this is the only possible Possible sobriquet left available. This is a dupe, for, in alphabetical order, Aim (moniker Aimee, Amy, Amee, etcetera), Denim, Joakim, Kimatra (moniker Kim), Kimimela (moniker Kim), Marrim, Maxim / Maxima / Maxime (moniker Maxim), Mimi (moniker Mim), Nimisha (moniker Nim), Pim, Rimona (moniker Rim), Simba (moniker Sim), Temima (moniker Tim), Timberly (moniker Tim), Timothea (moniker Tim), Ultima (moniker Ultim), Vimala (moniker Vim), and Ximena (moniker Xim) are easily potential candidates, and it also is a dupe for the reason the maternal side of Kim's family has shown no evidence of adopting the "impossible" paronomasia since, if they did, it would imply verboten relations inappropriate for a children's show, which is likely why the KP crew strayed away from any nominal assignment. Thusly, "Sim Possible" as a derivative of Simone, while plausible in and of itself (Timothea and Timberly perhaps equally so), is, ironically, impossible, and anybody who claims it is the only name, ironically, possible, is a sophist. Over the course of the show, she was never provided a name, nor was a name considered.
Confidence: 99