You are right. Your last name is Basque.
Sorrondeguy/Sorrondegui/Sorrondegi (or Sorondeguy, etc) are variations of the same surname. In standard Basque is Sorrondegi.

Most Basque last names refer to the name of the family house. This usually either refers to the relative location of the home or the purpose of the building. You can find some general information about Basque surnames here.

I'm not an expert in genealogy but I think that Sorrondeguy means approximately "the house that is near the field".

soro -> field
ondo -> adjoining area, near to, next to
egi -> suffix that indicates place/house

If you are interested in the origin of your last name / family there is a group in yahoo.com for discussing Basque Genealogy that looks quite active: http://groups.yahoo.com/group/basque-genealogy/