It's nice that you feel that way. However, "Atheism", is commonly accepted for what its original intended use which is to describe only those who believe there is no God. This implies the belief in true and false. Those who believe there is no such thing as true and false cannot take up a true/false position. As such, they are not atheists.The term "atheist" fits everyone that does not believe in any God, for whatever reason or from whatever angle.
In my opinion the term "atheist" can be accurately described as "not a theist".
To label anybody that does not believe in God as "atheism" is just as silly as labeling anybody that does not believe there is no God as "theism".
True/False is the basis for logical thought. Logical reasoning is used to come to conclusions of truth or fallacy.
Subjectivism is the belief that there is no such thing as objective true/false.
Skepticism is the belief that there is such thing as objective true/false, but man can never obtain knowledge of true/false.