A short form of Marilla, a form of Muriel, meaning "bright sea." Maxilla Cuthbert is a character in L. M. Montgomery's Anne books. Rilla Blythe in those books is named after Marilla.
Rilla is probably most often a short form of Marilla, which is itself a short form of Amarilla, which is a Latinate form of Amaryllis which was regularly used in the USA and Canada during the late 18th and early 19th centuries. [noted -ed]