Yes. See the /e modifier in perlre:

foreach $name ( @names ){
    $name = ucfirst($name); # made first letter  
    $name =~ s/\_(\w)/\ uc($1)/ge; # Here is the point.  
    print "$name \n";
}
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You can also change that to:

foreach $name ( @names ){
    $name = ucfirst($name); # made first letter  
    $name =~ s/_(\w)/ \U$1/g;
    print "$name \n";
}
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to avoid the /e. Also, see perlre again for \U and \L.