Sabba was borrowed into Hebrew from Aramaic, and while in Aramaic it means "old man", it means "grandfather" in modern Hebrew, just like how "Zaken" in biblical Hebrew means both old man and grandfather.
I disagree with the above poster- "old man" isn't a "daft" meaning for a name. In some cultures and time periods, old men are/were greatly respected. The meaning can imply that the person is experienced. I understand how people are turned off by the meaning, but they will (hopefully) be old one day too. I think the history behind this name is really interesting. Both Spanish and Greek, derived from Hebrew, and used on saints ranging from a Cappadocian hermit (Sabbas the Sanctified) to two Goth martyrs (Sabbas the Goth and Sabbas Stratelates) to the patron saint of Serbia (known as Saint Sava). Wow. I'm not Christian or even religious at all, nor am I Greek, Spanish, Turkish or Serbian, but man that's interesting at the very least. I think this name is of course usable, especially if the parents are anything listed above. The name doesn't look complex, but it is.