I signed a quit claim deed and had it notarized. I did not send the signed copy to my lawyer nor report it to the record or deeds. I do not want to go through with having my name on the deed after all. Is it safe to assume that since it is not recorded it is not a legal binding document? Thank you

A quit claim deed transfers ownership from the current owner to a new owner. It is not necessary for the new owner to sign the deed. Since you stated that you don't want your name on the deed, that implies you were not the previous owner.

If the previous owner signed it, they can register it unless you have the only copy.

It would help us help you if you explained more of the circumstances.

... Is it safe to assume that since it is not recorded it is not a legal binding document? Thank you

Assuming, as ScottGem does, that you are the grantee ("new owner"), it would depend on what you mean by "legal binding".

If, as between the grantor and the grantee (you), you own the property, yes. If the grantor delivered the deed to you it's your property. However, if you do not record it, the grantor could sell it to a third person (also assuming the third person didn't know about your deed) and that third person would own it would own it.

For real property purposes, the taxing entitly wouldn't know about it and would continue to send the tax bills to the old owner. At least until the old owner objected, saying "I sold it to Katmeg2, and here is a copy of the deed".

At any time in the future you could record it.

If you were to file bankruptcy, you would be obligated to schedule the property as your asset.

So, you see, there is a lot of "assuming" necessary to answer your question, and it depends upon what you mean by "legal binding".

The question is, who would know about the quit claim deed if I did nothing with it? I am the only one with the signed and notarized copy. My Grandfather will not do anything because he doesn't have the quit claim deed. He will do what is best for me he said.
The original deed states his name and his sons name. Now I've signed and notarized the quit claim deed but I'm the only one with this signed copy. I do not want to follow through with my name being put on the deed. I would rather inherit it in the end. Would it be beneficial to tell my lawyer all this information while my Grandfather is still living? Also, I thought in the state of PA it had to be documented in the record of deeds for the quit claim to be active. In other states that is not the case.

The original deed was in your Grandfathers and father's names? Did your father sign it also? How is the deed worded? Did you grandfather just deed his share?

How did you sign it? As I said it is signed by the owner(s) conveying the property to someone. But until you register the current deed remains in effect.