Is there a Latin name with the meaning fourth?

Yes, there are a couple of Latin words that refer to "fourth":

* quartus: This is the most common and straightforward way to say "fourth" in Latin.

* quater: This word means "four times" or "fourfold," but it can also be used to refer to the fourth position or instance.

So, depending on the context, either quartus or quater could be used.

For example, if you were talking about the fourth day of the month, you would use quartus dies mensis. If you were talking about something happening for the fourth time, you could use quater factum est.