grammaticality - Proper way to handle plurals with “whose”

I came up (re)phrasing a question like this:

What's so special about directories whose name begins with a dot?

But now, I'm wondering whether this is the correct handling of plurals or not. Should the following be preferred?

What's so special about directories whose names begin with a dot?

^{(In French both are correct and have different meanings — singular suggests that each directory has one name, plural suggests each directory can have several names, but it might be different in English.)}

Answer

The second is correct in this context. Since whose is referring to the plural directories, it must take a plural noun:

What's so special about directories whose names begin with a dot?

The above holds unless the directories collectively have one name, in which case it would be correct to use name in the singular.