@Allets: Basically you can't add anyone via a nickname as it works in other gaming networks. Both of you have to enter each other's Wii code to your friend list to be able to play with each other and send messages, so you're pretty protected from random spammers.
@Tinako: I found mine (via the message menu) - it's 7474-4738-8519-6211.
I don't play Wii that often, but anyone else also feel free to add me, I think I have like 5 people on my friend list.