The correct spelling in Scots Gaelic is Iain. Ianis an anglicization.
Uilleam is the Gaelic spelling for William.
If that is the correct spelling, it is not Gaelic.
In Scottish Gaelic it is spelled Mòrag.
Irish (Gaelic) is Seán or Eoin; Scottish Gaelic is Iain.
Easáias (from the Irish Bible); Isaiah in Scottish Gaelic.
CAITLÍN in Irish; in Scottish Gaelic, CAITLIN
It is just spelled Eric.
In Scots Gaelic MacAulay is MacAmhlaigh; 'the MacAulays' however is Clann 'IcAmhlaigh.
The spelling doesn't appear to be correct.