When you read the names from a database (I presume you are using a database as this is a database forum), you output the id of the name next to the link, for example;
echo "<a href=\"showname.php3?nameid=$row[id]\">$row[name]</a>";
Put this is some kind of loop when reading the output from the table and then in your showname.php3 script, you just need to go back to the table with the id to get the persons details.
Andrew