Welcome to the Asana Community @Sandra_G!
In the iOS app on the bottom you have „home“, „my tasks“, „inbox“, „search“ and „account“
Under „home“ you can easily access all projects, portfolios and goals.
Under projects you can then also see all, favorites or just the ones you recently accessed.
You can also locate projects very fast via the search.
See under „account“ there it shows which org you are currently logged in to and you can easily switch org (if you have the emails connected).
If you use completely separate Asana accounts that means you would have to log out to then be able to login to the other one. If that is a feature you are interested as well then I recommend upvoting this existing feedback request thread: Switching Between Multiple Asana Accounts in iOS
Does this help?