Shortened version of DBA?
Actually, I would presume that "Super Long Leaf Tea Company, LLC" is the full name of your company, not a DBA (since DBA names cannot use entity identifiers such as "LLC").
If you want to use ANY other name (such as "Super Long Leaf" or "Super Long Leaf Specialty Tea Shop") and associate those names with your company, you need to register DBA for each of those names. Depending on the state of your company registration, DBAs would be registered with Secretary of State, county clerk, or town clerk (or, like in Texas, with both Secretary of State and county clerk).
Either way, we can help you with all your DBA needs here.