For "skepticism about whether a concept is meaningful", agnosticism seems a good fit :-
"Agnosticism is the view that the truth values of certain
claims ... are unknown or unknowable."
On the other hand, if one "believes that the term "God" has no definable referent" then it could be atheism :-
"Atheism is, in a broad sense, the rejection of belief in the
existence of deities. In a narrower sense, atheism is specifically the position that there are no deities."
However, this is a philosophical nonsense because you would have to have an established concept of deity in order to assert that it does not exist. If the assertion is that the concept of deity is without standard or meaningful definition then you could qualify the position as "conceptual atheism" : the position that there is no workable definition of deity. Likewise, if the issue (as stated in the title) is "skepticism* about whether a concept is meaningful", then this could be "conceptual agnosticism".
* Skepticism, as in "refraining from making truth claims".
In matters of specific definition, it is worth noting that the Catholic encyclopedia is somewhat flexible about the existential definition of the essence of God, allowing for different philosophical world views :-
"It does not, however, appear to be a matter of great moment, as Soto
remarks, whether one holds or rejects the doctrine of a real
distinction between essence and existence, so long as the difference
between God and His creatures is safe-guarded, in that existence is
admitted to be of the essence of God and not of the essence of
So perhaps to be too literal in seeking a standard and precise definition is to be misled by language. For instance there is ambiguity in the definition of "universe",
where people go on to speak of multiverse. Other concepts similarly depend on various conceptual world views or (universe views).