With regular expressions you can often choose the easy way or the hard way. Although it's tempting to try and solve the whole problem with a single regular expression, that is often the hard way and the easy way is to take a step back and use multiple simple expressions instead. Consider:

use strict;
use warnings;

my @strings = split "\n", <<STRS;
Context Servername
Servername Context
Servername DBServer
Context Servername BogusServer
STRS

for my $str (@strings) {
    next if $str =~ /Context\s+Servername|Servername\s+Context/;
    next if $str !~ /Servername\s+(\w+)/;
    print "Matched: $1\n";
}
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Prints:

Matched: DBServer
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