Adapt to existing beos table in database sternwarte

Column mapping: id, name/vorname, kürzel (with umlaut), pw instead of
the planned schema. DB_NAME changed to sternwarte. create_table.sql
no longer creates beos, only the three new logbuch tables.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/auth.ts

@@ -2,16 +2,17 @@ import bcrypt from 'bcryptjs';
 import { query } from './db';
 
 export interface Beo {
-  ID: number;
-  Kuerzel: string;
-  Name: string;
-  Passwort: string | null;
+  id: number;
+  name: string;
+  vorname: string | null;
+  kürzel: string | null;
+  pw: string | null;
   MustChangePassword: number;
 }
 
 export async function getBeoByKuerzel(kuerzel: string): Promise<Beo | null> {
   const rows = await query(
-    'SELECT ID, Kuerzel, Name, Passwort, MustChangePassword FROM beos WHERE Kuerzel = ?',
+    'SELECT id, name, vorname, `kürzel`, pw, MustChangePassword FROM beos WHERE `kürzel` = ?',
     [kuerzel]
   ) as Beo[];
   return rows[0] ?? null;
@@ -24,15 +25,19 @@ export async function verifyCredentials(
   const beo = await getBeoByKuerzel(kuerzel);
   if (!beo) return null;
 
-  if (!beo.Passwort) {
+  if (!beo.pw) {
     const valid = password === 'logbuch123';
     return { beo, valid };
   }
 
-  const valid = await bcrypt.compare(password, beo.Passwort);
+  const valid = await bcrypt.compare(password, beo.pw);
   return { beo, valid };
 }
 
 export async function hashPassword(password: string): Promise<string> {
   return bcrypt.hash(password, 10);
 }
+
+export function getBeoDisplayName(beo: Beo): string {
+  return beo.vorname ? `${beo.vorname} ${beo.name}` : beo.name;
+}