The access credentials as well as database server host name and port are stored in a file in <LiveAgent_installation_folder>/accounts/settings.php
When you need to change the password for access to database, copy the original value of DB_PASSWORD and set it to a new setting named ENCRYPTION_KEY.
Since version 126.96.36.199 the database password is used also for encryption of passwords and keys stored in the database. If found in the settings.php file, the ENCRYPTION_KEY is used to encrypt and decrypt the passwords, keys and tokens of third party serviced (e.g. mail accounts), but also API keys stored in the database. If there is no ENCRYPTION_KEY, the DB_PASSWORD is used for this purpose.
If you should change the original DB_PASSWORD without setting the ENCRYPTION_KEY your LiveAgent installation would essentially stop working, since the software would no longer be able to decrypt saved password and keys.
DB_HOSTNAME=localhost DB_USERNAME=root DB_PASSWORD=newp@ssword DB_DATABASE=liveagent ENCRYPTION_KEY=pa$$word