If they have the ip, username and password to your server and it hasn't yet been setup then there are no database credentials yet. Isn't that what they're going to setup? If not then maybe they're expecting you to set it up. If you built the server from a LAMP image you probably defined it during the installation process. If you've forgotten what your root password is and you're still going to use MySQL you can reset the password.

It's really hard to give you an accurate answer without knowing more about the situation. Sorry.

If this is a freshly deployed droplet, you'll need to install & configure the web server (Apache, NGINX, etc), the database & client server (i.e. MySQL), PHP, etc. The droplets are bare-bones systems and only come with what the OS template ships with, which is basically just enough to get the Droplet running and allow you to SSH in to begin installing what you need.

Before you'll be able to provide them with credentials to the database, you'll need to make sure everything is setup and running properly.