The world has come to an end- or is just beginning. Either way, you are responsible for creating a new culture.
Tell us about it!

My island culture is named Magrethea, in honor of Douglass Adams and Hitchikers Guide to Galaxy. (Magrathea is the planet culture responsible for creating worlds.)
My language is English. It is a verbal language as well as a sign language. Spoken language is fine for subtle meanings, close contact conversations and teachings/singing. Sign language also adds a lot of subtlety, and can be used at a distance. Since we have to hunt, farm and maybe migrate, sign language is necessary. Also, any contact with outsiders could be easier with sign language.
Music would be important as a socializing, unifying and teaching tool. Simple instruments would be encouraged. Music and other useful professions would be assigned to guilds which anyone who qualified could apply for and enter.
Clothes would be loose fitting. Loose pants and shirts, smocks, robes, etc. Animals and plants would provide the materials.
Religion would be general. Belief would be encouraged without an organized guild which could get power/money hungry or too powerful controlling the people.
No currency. Trade and a policy of looking out for our own would be sufficent. This should also keep crime down.
There will be a guild for security. They will be police, judge, jury and executioner. They will be controlled by an assembly of guild leaders. Their costumes will reflect their skills and their level. They must know military strategy and a basic psychology as well as physical fighting skills. They will have their own secret sign language. This will help with crowd control, and during conflicts with outsiders.