This appears to work as requested, and it's a whole lot easier to read than some of the other options. :-)

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

my @words = qw( brian0 brian- -brian bri--an Bria-n br-i-an brian ) ;

print map { "[$_]" } @words ;
print "\n" ;

my @good = grep { 
                     /^[[:alpha:]]/ # Starts with a letter
                  && /[[:alpha:]]$/ # Ends with a letter
                  && ! /--/         # No consecutive hyphens
                } @words ;

print map { "[$_]" } @good ;
print "\n" ;
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Those who know that they are profound strive for clarity. Those who
would like to seem profound to the crowd strive for obscurity.
            --Friedrich Nietzsche