## C#, <s>498</s> 392 bytes ##

I just really wanted to do this with linq, too bad I had to write my own sum function for BigInteger that really killed it :-(

 using System;using System.Linq;using System.Numerics;using System.Collections.Generic;static class a{static void Main(){var f=new List<BigInteger>(){1,1};while(f.Count < 100)f.Add(f.Skip(f.Count-2).Take(2).Aggregate((a,b)=>b+a));f.ForEach(x=>{if(x%6==0)Console.Write("FiboNacci\n");else if(x%2==0)Console.Write("Fibo\n");else if(x%3==0)Console.Write("Nacci\n");else Console.WriteLine(x);});}}

Ungolfed:

 using System;
 using System.Linq;
 using System.Numerics;
 using System.Collections.Generic;
 static class a
 {
 static void Main()
 {
 var f=new List<BigInteger>(){1,1};
 while(f.Count < 100)
 f.Add(f.Skip(f.Count-2).Take(2).Aggregate((a,b)=>b+a));
 f.ForEach(x=>
 {
 if(x%6==0)
 Console.Write("FiboNacci\n");
 else if(x%2==0)
 Console.Write("Fibo\n");
 else if(x%3==0)
 Console.Write("Nacci\n");
 else 
 Console.WriteLine(x);
 });
 }
 }

Edit: Down to 392 bytes thanks to LegionMammal978 for the aggregate suggestion and thanks to olegz's C# answer for the x%6 shorthand for X%2 && x%3