You're looking at v1 documentation. The current version is v3. You can find the docs for the current version here.

Custom Database Names

If you want to specify the tenant's database name, set the tenancy.database_name_key configuration key to the name of the key that is used to specify the database name in the tenant storage. You must use a name that you won't use for storing other data, so it's recommended to avoid names like database and use names like _stancl_tenancy_database_name instead. Then just give the key a value during the tenant creation process:

>>> tenant()->create('example.com', [
    '_stancl_tenancy_database_name' => 'example_com'
])
=> [
     "uuid" => "49670df0-1a87-11e9-b7ba-cf5353777957",
     "domain" => "example.com",
     "_stancl_tenancy_database_name" => "example_com",
   ]