Die Namen sind normal. (The names are normal)
Would it be a more accurate translation into English understanding The names are traditional in this instance?
I think a better translation than normal would be "common", "standard", or "ordinary", but you probably could describe some of them as traditional too.
As in "John" is a more "normal" (i.e. common) name than say, "Trevor", or a foreign name. Though I suppose in English, traditional names tend to also be common names, such as John, William, or Mary. Although nowadays there are also uncommon "traditional" (or old-fashioned) names such as Clarence and Mabel.
It might depend on what kind of "name" it is. Most likely names for people, but it could also be the name of anything such as a title. I would say "traditional" would not be a standard translation.
I think there are similar connotations in German, i.e., "Die Namen sind normal" sounds a bit strange without context - it seems rude to (possibly) imply that somebody else's name would then be "not normal / abnormal"; you could use e.g. "gebräuchlich" instead ("common = widely used"), or, as you suggested, "traditionell", if that's what it's about. I can imagine a context where you could use "normal" without sounding rude, though; but one way or another, I suggest to just stick to the given words and translate "normal" with "normal".