Scottish form of William [q.v.] + -ina.
This name, like its variant Wilhelmina, is far from rare in the 1841 Census of Aberdeenshire, with nearly 20 minor variations in the spelling. To find these, it is recommended that Soundex searching for both Wilhelmina and Williamina should be used.
One correspondent [LPC] notes that Wilma can be used as a pet name for Williamina and another [BG2] has found Bill used. We also know of Billie being used as a pet name.