So, what is the output of the program when run through the browser?

Also, what is the output in the web server error log? You print to it in the case of an error, but maybe you want to also signal this condition to the browser, even if only for debugging?

open (FILE, ">>$db") or print STDERR "[$0] Could not open file! $!";
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... should either be

open (FILE, ">>$db") or die "[$0] Could not open file! $!";
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or should be something like:

if( open (FILE, ">>$db")) {
    print (FILE "Name:$name,Surname:$sname\n");
    close (FILE);

} else {
    print STDERR "[$0] Could not open file '$db': $!";
    print "<b>Sorry, an error happened: $!";
};
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