Translation:The ancient name is for a more ancient city.
If you translate the first "antico" as "former," which is an accepted translation, it might make more sense: "The former name is for an older city." For example, "New York" was once called "New Amsterdam." That name was for a much older city (more like a town, actually), not the city we know today. http://en.bab.la/dictionary/italian-english/antico
First I wanted to write that too, but I am aware that the Italian Duolingo training database prefers literal translations and there is no "even" in the Italian sentence. I ended up writing "The old name is from an older city." which I wouldn't normally say. I would write it with "even" too.
To me it looks like translations that contain all the words from the Italian with no extra words are preferred over good translations. Pretty sad, isn't it?
Well, if you add extra words like "even", then you select a specific meaning and context for the sentence. If you leave the nice words out that put the sentence exactly right, then the sentence might be a valid translation for a bigger range of meanings. It is less specific and more likely to hit the context which the author of the original translation was thinking of.
When we know what the Italian sentence is supposed to mean, then we can be as specific as we want and give good translations that totally make sense and are enjoyable to read without leaving confusion in the mind of the readers like "wtf should that mean?". Good luck with your learning!