Difference from hurricane deductible
A hurricane deductible applies only when the storm is classified as a hurricane. A named storm deductible applies to any named system: tropical storm, subtropical storm, or hurricane.
Some Florida policies carry a named storm deductible specifically to broaden the deductible-application window. Review your declarations page: if "named storm deductible" is listed, that's the applicable trigger.
Application
When a named storm (e.g., Tropical Storm Fay, Subtropical Storm Debby) causes damage, the named storm deductible applies: typically 2-5% of dwelling coverage, like the hurricane deductible.