Should you cite a paper that clarifies the name of a mathematical object? Suppose I am writing a mathematics paper and discover some object and call it a "thingy"; not knowing of its existence outside of my discovery of it. 

Later while doing some unrelated research I come across a paper that uses my "thingy" and it turns out to be well known object called a "doodad". 

Should I cite the paper that gave me the vocabulary to describe a well known object if it only gave me its name?

This is my first real paper so I want to get my citations right.
It is not wrong to cite the paper which clarified the term. In fact you must if you were to imply or use the definition that the paper provides.

A technical term may have multiple definitions in which some may even redefine it in different fields and aspects. It would be better to cite the one that connects to the most appropriate definition that connects to your use of the term.