C#, 498 392392 320 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 < 100Count<100)f.Add(f.Skip(f.Count-2).Take(2).Aggregate((a,b)=>b+a));f.ForEach(x=>{if(x%6==0)ConsoleSystem.Write("FiboNacci\n");else if(x%2==0)Console.Write("Fibo\n");else ifWriteLine(x%6==0?"FiboNacci":x%2==0?"Fibo":x%3==0)Console?"Nacci":x.WriteToString("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 < 100Count<100) f.Add(f.Skip(f.Count-2).Take(2).Aggregate((a,b)=>b+a)); f.ForEach(x=> { if(x%6==0) ConsoleSystem.Write("FiboNacci\n"); else if(x%2==0) Console.Write("Fibo\n"); else ifWriteLine(x%6==0?"FiboNacci":x%2==0?"Fibo":x%3==0) Console?"Nacci":x.WriteToString("Nacci\n"); else Console.WriteLine(x); }); } } Edit: Down to 392320 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 as well as the use of ternary operators in a single WriteLine statement.