The following article tells that the "default" Redis server configuration in Azure has 16 Redis databases: https://msdn.microsoft.com/en-us/library/azure/cbe6d113-7bdc-4664-a59d-ff0df6f4e214#RedisConfig.
It also states that:
Any values that are configurable, such as max-memory-policy, are configurable through the portal.
As for me I've not found such setting in Azure Portal.
Is it possible to change amount of Azure Redis databases?
As mentioned by Pranav, this is not yet possible, but is something we are considering in the near future.
Update: Yes, we rolled this feature out, but it isn't a configuration setting, it is a limit based on the size of cache instance you have chosen. For instance, a C1 still has a limit of 16, but a C4 has up to 32. See https://learn.microsoft.com/en-us/azure/azure-cache-for-redis/cache-configure#default-redis-server-configuration for more details