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In Lord of the Rings the Wizards have a name and then a color, I was wondering if those colors held significance to a rank if so please tell me.

They do and they don't just to be awkward. Gandalf the Grey is seen to be wearing grey even before he came to Middle-Earth as the Maia named Olorin he is seen to be waring grey. Radagast, called Aiwendil in the West wears brown this is mostly due to his earthly nature and his harmony with land and beast rather than rank.

Saurman, Curumo in the West wore White. The council was called "The White Council" and Saurman was its head this is the only colour that may be seen as defining rank, the fact that Gandalf takes up the white robes is more symbolic of him replacing Saurman and taking over as head of the order. There are also two Blue Wizards Alatar and Pallando the blue robes they wore don't seem to show any specific significance.

There is also a possibility that robe colours could be drawn up primarily to the Valar division they were in (excluding the White)

Olorin/Gandalf: Manwe and Varda
Radagast: Yavanna
Alatar and Pallando: Orome

Its also interesting to note that Curumo/Saurman was a Maia of Aule the Smith. As was Sauron. Both fell to darkness, this could be something to due with the nature of Aule as even though they were not in Erus plan Aule made the Dwarven folk and Eru chose to gave them life. Whilst the Maia of Aule would not have his control and may be more likley to fall to darkness.

And it could have something to do with Saruman wanting more power and denying Saruman the White to go with Saruman of the Many Colours. He wanted the One Ring and was mad that Gandalf recieved an Elven Ring of power and he didn't.