#Pyth, 51 bytes

    V.Wn100lHaZ+@Z_1@Z_2[1 1)|+*"Fibo"}2JPN*"Nacci"}3JN

Generates the Fibonacci sequence then decides what to print. 

                        [1 1)                           - H = [1,1]
      Wn100lH                                           - While len(H)!=100 
             aZ+@Z_1@Z_2                                - H.append(H[-1]+H[-2])
    V.                                                  - For N in H:
                                        JPN             - Set J to the prime factorization of H
                               *"Fibo"}2J               - If there is a 2 in the factorization, add "Fibo" to a string
                                           *"Nacci"}3J  - If there is a 3 in the factorization, add "Nacci" to a string
                              +                         - Join them together
                             |                        N - If the string isn't empty (If it isn't divisible by 2 or 3), print N
                                                        - Else print the string

To test, try this (only does the first 20 numbers)

    V.Wn20lHaZ+@Z_1@Z_2[1 1)|+*"Fibo"}2JPN*"Nacci"}3JN