To date the search bar in Storemapper searches exclusively for a location and does not look at business names.
In our experience, searching by name is almost never useful for the customer. Customers arrive at the store locator page specifically because they don’t know which businesses are your retailers, if they knew the business name they almost always go directly to native Google Maps and look for it there.
If you need another way to filter the search, we recommend using category filters.
That said, we do keep a very open mind, if there is something about your business where it really makes sense for your customers to search by name. Please message us and let us know.