#!/usr/local/bin/perl
use strict;

use Getopt::Long;
use sql_engine;
my $string = "XXX2EX_";
#my (@grepnam, @names);
while(<>) {
 chomp;
 if ($_ =~/SNP*/i) {
  
  #print $_, "\n";
  if ($_ =~s/BM*/$string/) {
  
   print $_, "\n";
   
  }
   
} 
  
}
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In your code this line if ($_ =~s/BM*/$string/) substitute BM* with the literal string XXX2EX_ having it in the variable $string, to prefix XXXXX change the second if condition as  if ($_ =~s/(BM*)/XXXXX_$1/)