Save each line of input to a variable and compare the variable like:

    # get input 
    $input = <STDIN>;

#----------------------If user Picks 1-------------------#
    if($input == int 1)
    {
        system "cls";
        $fname = "";
        while ($fname eq "")
        {
            printf "\n\nPlease Enter your First Name: ";
            $fname = <STDIN>;
            chomp($fname);
            &menu;
        }#end of while loop    
    }#end of if();
#----------------------If user Picks 2-------------------#
    if($input == int 2)
    {
        system "cls";
        $lname = "";
        while ($lname eq "")
        {
            printf "\n\nPlease Enter your Last Name: ";

            $lname = <STDIN>;
            chomp($lname);
            &menu;
        }#end of while loop    
    }#end of if();
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Update: samtregar beat me to the punch