I just go for the blatantly obvious and simple, especially since I tend to end up over time with various versions of sites and their associated databases. So, for example, the main site I work on, called BLUF, is presently in its fourth incarnation, and the MySQL database is called BLUFv4. Another site, called stimbroker has a database with the same name, and for another site, I have the current iteration named itpaV3 and the previous one itpaV2 is still hanging around. So, I'd say, just call them what you want.
If you want to keep things simple, name them like packages, eg com.mycompany.myproject so you can at least see what project they are for easily.
I'd personally strongly advise against using a password generator, because a) you'll curse yourself one day when you're looking at your list of databases in MySQL trying to remember which project uses the database called P34Ed9wkyqUP, and b) you'll very quickly become tired of having to copy and paste it whenever you need to write some code that references the name.
That said, to an extent the database name is largely irrelevant, because other than when you set up the connection to it, you can assign it to whatever easy to remember variable name you want in your code, whether that's server side in php or in B4x when you're dealing with a local database file. It's probably more important to make sure the tables are clearly named, with titles that will help you to remember what's in which table when you're writing queries in six months time.