Can Cloning an object cause a "Memory Leak" of sorts

I’m cloning an object a lot but making sure that no more than 3 of the objects is in the game at one time. The problem that I am facing is that each clone is labeled “Object(Clone)”
and every time another one of that object is instantiated into the game it is called “Object(Clone)(Clone)”. This repeats until I have a huge number of “(Clone)”'s in the objects name. Could this cause a performance issue if left unchecked?

If you are concerned you can always reset the name after each instantiate.

GameObject clone = (GameObject)Instantiate(myObject);
clone.name = myObject.name;