This is likely a nickname shortened from the phrase "mine Oll" (Oll or Ol being a short form of Oliver already). As English changed and the correct phrase would've become "my Oll," the 'n' was mistakenly placed with the name rather than with the possessive 'my' to preserve the previous sound. This is also where the names Ned ("mine Ed"), Nan ("mine Ann"), and others originate.
I never knew 'Noll' is a pet form of the name Oliver! I guess you do learn something new everyday. Noll isn't used as a traditional nickname as much as it used to. I prefer the cute nicknames Olive and Olly. :)