For a shop that sells flowers and plants, you can use either "florist" or "florist's" below the official name. Both options are correct, but they have slightly different connotations:
Florist: This refers to the profession or business itself, indicating that the shop specializes in flowers and related services. For example, "Sunshine Florist" suggests that the shop offers floral arrangements and other related services.
Florist's: This is possessive and suggests ownership or a specific place belonging to the florist. For example, "Sunshine Florist's" implies it's the shop owned by a florist or associated with a specific florist.
The choice depends on your cousin's preference for how she wants the shop's name to sound. Both are commonly used and understood by customers.