Yes, the plugin is capable of searching stores by their names. The administrator has the option to enable either search by address or by stores names. Moreover, the option is provided in “ASL Settings” as shown in the image below.
Image of Search by Store Name Option
You can also include this feature by the shortcode attribute “search_type”, the complete shortcode for search by store name option is the following:
[ASL_STORELOCATOR search_type="1"]Demo of Search by Store Name.