～という意味 is used to show what something means.
We have seen that when used at the end of a sentence, ～という means “to say…..”
However, 言う can also be used like this:
彼はデーベッドと言います。
He’s called David.
This is not about what David is saying, but what he’s called. 言います can be changed to the plain form to modify other nouns like this:
デーベッドと言う人も言いました。
Somebody called David was there.
In a wider sense, X と言う B can mean “B that is described by / called / X”. In the following example we’re talking about “red”, and saying it has a meaning that is described by “stop”
赤は止まれという意味です。
Red means stop.