The Default Text used in the Source field seen in the DNN Search Drop Down or Search Results is Set from the Module Definitions Friendly Name.
I think this should be the ultimate Fallback but there are a number of modules available that are multipurpose and used for various parts of a website. e.g. an article module could be used for News, Events, Testimonials, Case Studies, Projects on just one website on different pages.
There needs to be a method of nominated what the source is on a tab module by tab module basis or at least on the search results settings.
The best option would be to a setting on each tab module instance that nominates what to use when indexed as the source, or alternatively In the search results settings a similar setting should be available to nominate the source as the module definition Friendly name, the Module Title or even better a configurable field on the module (as sometimes you want it to be different to the module title)
An article module is on the home page with module title Case Studies, in the search source i would want this to come up as Feature Case Studies as there is another Case Studies page that is the full list of case studies and the module is also used for news and testimonials on the same site.
The Source definitely wouldn't want to have "News,Events Testimonials,Case Studies etc." which is what you would have to name the module definition friendly name for the module as it is used in so many areas of a website
hope it makes sense