The letter is known as "tzadik" in yiddish, and hebrew speakers often give it that name as well.
This name for the letter probably originated from a fast recitation of the alphabet (i.e., "tzadi, qof" -> "tzadik, qof"), influenced by the hebrew word tzadik, meaning "righteous person".
The origin of tzadi is unclear. It may have come from a middle bronze age gliph based on a pictogram of a plant, perhaps a papyrus plant, or a fishing hook (in hebrew, tzad means "[he] hunt[ed]", and in arabic sad "[he] hunted".
As an abbreviation, it stands for tzafon, north.
Each jew is obliged to donate mahatzit hasheqel, half sheqel, to the tabernacle, in order to espiate. The tzadi in the middle of the word mahatzit, half, means tzedaka, beneficence. Next to it the are two letters, the het and the yod. Together they form the word hay, life. On the other hand, the letters in the beginning and in the end of the word are mem and tav. Together they form the word met, death.
This indicates that by giving beneficence one keeps the life close and death faraway. (source: Gaon from Vilna)
Righteousness and humility are the two defining traits of the tzadi. The shape of the tzadi is a nun with a yod riding on top it. This signifies that the yod, Essence of the Creator who animates all matter, guides and dwells with the one who is humble, as symbolized by the nun.
Below you can see a movie of me doing in clay the first prototype of a hebrew letter, prototype which willl later be 3D reduced to the size of a jewel.