Greetings from the Academy of Saint Gabriel!
You asked for a 12th to 14th century Gaelic form of <William>. Here is what we have found.
In your period, Gaelic was spoken in both Ireland and in the north and west of Scotland. Naming practices were very similar in the two areas, but not quite the same; and they did vary over the three centuries you mentioned. We will give you information in this letter about the given name you've chosen. If you can narrow down the time and place you want your name to fit, we would be happy to help you further.
The name <William> was brought to the British Isles by the Normans. The Normans reached Ireland in the 12th century. The Irish adopted some names from them, but not immediately. <William> made its way into Irish usage as <Uilliam>, pronounced almost the same as the English form, but probably not until the late 13th century. The diminutive form <Uillec> is recorded in the early 14th century .
The Normans brought the name <William> to Scotland as well, and it was adopted into Gaelic culture by the mid-12th century. The Scottish Gaelic form of the name was <Uillem> . Records from this period are uniformly written in Latin and, somewhat later, in Scots. (Scots was a language closely related to contemporary English.)
Men in Gaelic culture were most often known as their father's sons, such as <Uilliam mac Dhomnaill> "Uilliam, son of Domhnall". This sort of byname is called a patronymic. Although some men were known by physical characteristics or by the places where they lived, they would also have used patronymic bynames as well. Once you know where and when you want your persona to live, we could suggest some likely names for your father.
I hope this letter has been useful. Please write us again if any part of it has been unclear or if you have other questions. I was assisted in researching and writing this letter by Talan Gwynek.
For the Academy,
 Donnchadh O'Corrain and Fidelma Maguire, Irish Names (Dublin: The
Lilliput Press, 1990).
 Black, George F., _The Surnames of Scotland: Their Origin, Meaning and
History_, (New York: The New York Public Library, 1986).