[eothain of fenland]

I've always thought that the Gondorians spoke Sindarin, but after reading the appendices in the back of the third book, I found out that they primarily spoke Westron, the COmmon Speech. So, did they have Westron names? or would they speak the common tongue but call one another in their Sindarin name, much like we do in English? (not Sindarin of course)

Thanks