The word "Rastignac" originates from the name of a character in Balzac's "Pere Goriot". What does this word mean and how does it relate to the character?

Rastignac is the character's last name.

https://en.wikipedia.org/wiki/Eug%C3%A8ne_de_Rastignac

To clarify from Shadowmyst2004 reply:

A Rastignac is a social climber, or sort of nouveau riche, that grows from a looked down upon social class to an upper social class through scheming, fawning, or generally disingenuous means. As mentioned, the character this trait is named after has the last name of Rastignac. As the wikipedia article Shadowmyst2004 links, it shows how across various books in the La Comedie humaine series, and others written by Balzac that the character climbs the social ladder as he goes from low social class to high.