Well there are a ton of Scots Families that have been in Ireland for multiple generations. My own grandfather of line was one of them. In order to hold the land grants given to these Scot families, you had to stay for 5 years. Grandfather Bernard Lindsay did, and then promptly returned to Scotland, but many stayed. Your Dixson name was created (son of Richard , or son of Dick, the short name for Richard) by the Keith family, High Marshals of Scotland.
Capt Joseph Lindsay Haley III Esq ATP FSA Scot. I have access to the Libraries of Scotland's National Museum.and archives.