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Greetings,
We don't have any reason to contradict the information you got from Laurel. We have no reason to believe that "Connor MacLiam" is a medieval name--we don't have any period examples of "Liam." Laurel has already provided a list of variant forms.
The only comment we can add is that "MacLiammoir" is also not a period name. "MacLiammoir" is a post-period construction which was created by the Willmore family, who tried to "translate" their name into Gaelic.
If you're looking for other alternative names, a good, but not perfect, source is any book by Edward MacLysaght. Not all of the names he lists are from the Middle Ages, but we can do further research on the names he lists to see whether or not they're medieval names.
Tangwystl verch Morgant Glasvryn, Margaret Makafee, and Pedro de Alcazar contributed to this letter.
We hope this has been helpful, and that we can be of further assistance.
In service,
Alan Fairfax
Academy of S. Gabriel