Du hast einen Fehler in der mail() Funktion.
mail($empfaenger, $betreff, $nachricht, $mailtext);
In den letzten Parameter gehört der Header mit Absender, z.B. so:
$header = 'From: webmaster@example.com' . "\r\n";
Den Namen kannst Du an die Variable $nachricht dranhängen.
<span class="syntaxdefault"><br />$empfaenger </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxstring">'info@riensartwork.de'</span><span class="syntaxkeyword">;<br /></span><span class="syntaxdefault">$betreff </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxstring">'Guestbook'</span><span class="syntaxkeyword">;<br /></span><span class="syntaxdefault">$nachricht </span><span class="syntaxkeyword">=</span><span class="syntaxdefault"> </span><span class="syntaxstring">" \nFreigeben: http://riensartwork.de/gaestebuch-freischalten.php?id='mysql_insert_id()'"</span><span class="syntaxkeyword">;<br /></span><span class="syntaxdefault">$nachricht </span><span class="syntaxkeyword">.=</span><span class="syntaxdefault"> </span><span class="syntaxstring">"oder Loeschen: http://riensartwork.de/gaestebuch-loeschen.php?id='mysql_insert_id()'"</span><span class="syntaxkeyword">;<br /></span><span class="syntaxdefault"> <br />$nachricht </span><span class="syntaxkeyword">.=</span><span class="syntaxdefault"> </span><span class="syntaxstring">"\nName: "</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">.</span><span class="syntaxdefault"> $_POST</span><span class="syntaxkeyword">[</span><span class="syntaxstring">'name'</span><span class="syntaxkeyword">];<br /></span><span class="syntaxdefault">$nachricht </span><span class="syntaxkeyword">.=</span><span class="syntaxdefault"> </span><span class="syntaxstring">"\nBeitrag:"</span><span class="syntaxdefault"> </span><span class="syntaxkeyword">.</span><span class="syntaxdefault"> $_POST</span><span class="syntaxkeyword">[</span><span class="syntaxstring">'eintrag'</span><span class="syntaxkeyword">];</span><span class="syntaxdefault"> <br /><br />mail</span><span class="syntaxkeyword">(</span><span class="syntaxdefault">$empfaenger</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> $betreff</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> $nachricht</span><span class="syntaxkeyword">,</span><span class="syntaxdefault"> $mailtext</span><span class="syntaxkeyword">);<br /><br /></span><span class="syntaxdefault">echo </span><span class="syntaxstring">'<h5>Thank you for your comment</h5><meta http-equiv="refresh" content="3; URL=test.php" />'</span><span class="syntaxkeyword">;<br /></span><span class="syntaxdefault"> <br /> </span>
Leider hab ich keinen Hoster zum Testen, falls es nicht klappt einfach noch mal melden.
LG