Obdulia Abarca is a Mexican politician from the Party of the Democratic Revolution. From 2009 to 2012 she served as Deputy of the LXI Legislature of the Mexican Congress representing Chiapas.
Obdulia Luna (? - 1980) was the first Ecuadorian woman to obtain a law degree. She graduated on June 15, 1928, at the university of Guayaquil. She worked as secretary of the first Chamber of the Superior Court of Justice of Guayaquil.
This name reminds me of the Latin-derived word *dulia*, meaning the "worship"/veneration given to saints, as opposed to *latria*, the worship given only to God. Not that I think *dulia* and Obdulia are necessarily connected - the Arabic etymology sounds much more plausible to me.
This name is probably an old feminine form of the Arabic name "Abdul," meaning "servant." This reflects how the Moorish conquest and Arabic language influenced old and modern Spanish language and culture.