Tine is the Irish word for fire.
"na Tine" means "of the fire" Sir isn't an Irish word.
The name Aiden means little fire in Irish (Aodhán). Otherwise 'tine bheag'.
tine
tine / dóiteán
tine lonrach
tine pronounced tin-e
In Irish it's "tine bheag"
Modern Irish - tine; Old Irish - teine Scottish Gaelic - teine Manx - aile The name Áed is another word for 'fire'. Delbaeth means 'fire shape'.
tine tempha
In Irish it's "bean na tine"
It's not an Irish name so it has no meaning in Irish.
It has no meaning in Irish; it's not an Irish Gaelic name.