You can do that by shuffling an array of names and coupling neighbors in the result. I've omitted the file I/O parts for clarity.

This imports an excellent shuffle() function, use List::Util 'shuffle'; This reads an array full of the names with numbers and dot stripped, and then strips newlines, too,

my @friends = map { (split /\./)[1] } <DATA>;
chomp @friends;
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Shuffle them and stuff them into a hash, which naturally pairs them,

@friends = shuffle @friends;
my %couple = (@friends);
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Finally, print the pairs,

for (keys %couple) {
    print "$_ and $couple{$_} are partners\n";
}
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Here's the "file" that code reads. To read from a named file, instead, just do as you did above.

__DATA__
1.bobby
2.jane
3.charleen
4.markus
5.gabriel
6.Alex
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Perl data structures and the shuffle function make this a lot easier.