Here's what you need to do to become a Warrior:
1) Have gone on at least one hunting patrol with their Clan.
2) Have gone on at least one border patrol with their Clan.
3) Have been given an assessment by their mentor.
4) Have been given battle practice and know how to use the battle system.
5) Have been to at least one Gathering.
When you have met all of these requirements, please pm your Clan leader and tell him/her that you have. They will hold your ceremony when they are ready. Also let them know what you would like your warrior name to be.
But, not only do you need to have met the requirements to receive your warrior name, but you need to be seen fit in the eyes of the other warriors that you deserve to be one.
P.S. At the moment, I have taken over all leader and some apprentice training duties. So please pm me if you have met the requirements. Read this for more information.