Something like this might work.

use strict;
use warnings;

while(<>)
{
  chop;
  my($id) = /\\\\.+\\(.+)/;

  print "$id\n" if($id);
}
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In the regular expression I use ()'s to group and capture, then because I used ()'s on the my, it puts a list context onto the assignment and so the RE returns a list of the captured values. In this case the first captured element returned is assigned to $id. I then use $id normally to print out the ID if the RE matched. On a non match $id is undef.

I tested with a tiny test case of:

\\domca-prn01\DH4-2139-HP4
\\vlasd
\\\dsasd
\test\ing
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Only the identifier from the first line of the test file is output.