... a ... regex solution for this problem?

Since the application seems to call for exact string matching, I would prefer a hash lookup or any-based solution as discussed already in this thread.

But a regex solution might look like this:

c:\@Work\Perl\monks>perl -wMstrict -le
"my $t1 = 'EV-1891';
 my $t2 = 'EV-DKL1';
 ;;
 my ($rx_name_set) =
   map  qr{ \A (?: $_) \z }xms,
   join '|',
   map  quotemeta,
   reverse sort
   $t1, $t2
   ;
 print $rx_name_set;
 ;;
 for my $name (@ARGV) {
   if ($name =~ $rx_name_set) { print qq{name '$name' in set}; }
   if ($name !~ $rx_name_set) { print qq{name '$name' NOT in set}; }
   }
"  EV-1891 FOO
(?msx-i: \A (?: EV\-DKL1|EV\-1891) \z )
name 'EV-1891' in set
name 'FOO' NOT in set
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Since the regex is  \A \z anchored for an exact match, the
    reverse sort
step isn't really necessary, but it can't hurt. See Building Regex Alternations Dynamically. As to how fast it is, I leave that to your Benchmark-ing. My guess is that this approach should be fairly fast if you don't have to build the regex anew each time you do a set of comparisons; if you do, forget it.