While I made the same association when first reading the books, I'll point out that the name Saruman is one the humans gave him. His Quenya name, Curumo, has little to do with Sauron, nor with the latter's original name Mairon before he revealed his allegiance to Melkor and the elves dubbed him Sauron (Quenya) and Gorthaur (Sindarin).

There is a connection between them, but it isn't by name. They were both originally Maiar of Aulë, both ambitious and cunning, both desiring order. But where Sauron thought siding with Melkor would get him the means to impose his noble order, Saruman stuck with the Valar and was eventually sent to protect the newly awakened elves from Melkor.

Still, that shared ambition for order eventually made allies of them, while their respective cunning saw each scheming against the other. If Gandalf and those meddling mortals hadn't gotten in the way, the final stage of the War of the Ring would have been a struggle between these two former colleagues. Depending on where the Ring ended up, that might have been an interesting struggle, the two most cunning Maiar going head to head, but I think it's for the best we never found out how that would have gone.