1, 2, 3, 4, 5, Shaggy

Python 2, 64 63 bytes

Anonymous function with arguments n and k, returns the list to output.

lambda n,k:[[i,'Shaggy'][i%k<1or`k`in`i`]for i in range(1,n+1)]

Alternatively, a function which prints to STDOUT for the same bytecount:

def f(n,k,i=1):exec"print[i,'Shaggy'][i%k<1or`k`in`i`];i+=1;"*n

Pyth, 25 23 bytes

m?|!%dQ}`Q`d"Shaggy"dSE

A program that takes input of two newline-separated integers k, n and prints a list.

Try it online!

How it works

m?|!%dQ}`Q`d"Shaggy"dSE  Program. Inputs: Q, E
m                    SE  Map over [1, 2, 3, 4, ..., E] with varaible d:
 ?                         If
    %dQ                    d % Q
   !                       negated is truthy (divisible by H)
  |                        or
        `Q                 str(Q)
       }                   is in 
          `d               str(d):
            "Shaggy"         Yield "Shaggy"
                           Else:
                    d        Yield d
                           Implicitly print

SQL (PostgreSQL flavour), 130 136 bytes

Done as a prepared statement:

prepare p(int,int)as select CASE WHEN i%$2=0or i::char like'%'||$2||'%'THEN'Shaggy'else i::char end from generate_series(1,$1)a(i)

This is executed in the following manner

execute p(20,6)

and the result is output as rows.