I believe you're asking how to discover whether your maternal grandmother was correct when she said your maternal grandfather's surname, Daniel, had been changed from McDaniel and was originally McDonald. My maternal grandmother was a McDaniel, and I have documentation that proves it was originally McDonald. Also, George F. Black, Ph.D., in his book "Surnames of Scotland", wrote that McDaniel is a corruption of McDonald that occurred mainly (but not exclusively) in the American South, owing to "a faint assonance" (similarity in vowel sounds) in pronunciation.
I assume you've already done census research. If you don't find your Daniel ancestors in a particular census, look for them as McDaniels and McDonalds. Aside from that, here's what happened in my family.
My 4th-great-grandfather Henry McDaniel fought in the Revolution, but neither he nor his widow ever filed for a pension. Eventually, their eldest son filed for a survivor's pension on behalf of himself and his siblings and, in order to do so, acquired a copy of the parents' 1788 marriage record. When it came, he was surprised that it showed his father's surname as McDonald and tried to have the court "correct" the marriage record. Apparently, his father had never bothered to tell the family that the name was originally McDonald. Fortunately, all of that was documented in the father's pension file with the National Archives and Records Administration.
What I did to confirm the change was to look for deeds where the family lived after 1788. Lo and behold there was a 1796 deed in which the father's surname was written both ways. At the same time, a distant cousin of mine researched tax lists for the county where the family lived prior to 1800 and found not only Henry but also his two eldest brothers listed sometimes as McDaniel, sometimes McDonald, and even sometimes McDanald. By the way, that was in the American South; i.e., Virginia/West Virginia.
Also, if you have not yet done so, I recommend you have a Family Finder DNA test with FamilyTreeDNA. Once results are in, you can look for matches who have Daniel, McDaniel, and McDonald surnames in their ancestry, try to establish communication with those matches, and find out if they have records that show a change from one to the other. Six of my siblings and I all have FamilyFinder tests. Wouldn't it be something if you turned out to be a match for us.