My name's Don Gillies and I live in Scotland. Your family (like mine) originated in an area of Scotland called Argyle, which includes the islands such as Islay, Mull, Iona, etc, but also on a part of the mainland known as the Mull of Kintyre, where there are a great many of your family.
The first thing to explain is that our ancestors spoke a different language to us - Gaelic.And your surname came from a man known as EachTighearna, which is Gaelic for horse-lord. The Gaelic for son is "mac", so his sons had the name MacEachTighearna. This name is pronounced in Gaelic as MacEckTerna.
With the Gaelic language starting to die out, and with people moving to different areas and countries, the name took on various changes, to make it easier to spell and pronounce for non-Gaelic speakers. And that is why there are now McCatherns, McEacherns etc.
As regards castles. One of the most famous MacEachTighEarna's was Colin, who was very important in the Mull of Kintyre and owned a large area of land. There are several castles in the area and the MacEachTighEarna's would I'm sure haved lived in one of them.
Coming from that area, the family would also have been close to and fought alongside the Campbell family, who are also known as the Dukes of Argyll. You will find their castle with a Google search for "Inveraray Castle".