Remember to search for both direct and indirect competitors. Industry classifications can be problematic, i.e. if you search for Indigo because you're interested in book sales, Amazon may not show up as a competitor as it is not classified in the same industry category.

If a potential competitor is a large conglomerate, it may also not show in your results because its primary industry is classified as something else, i.e. Mars Inc. may show up for candy but not for pet food, and there may be no industry classification connection for smaller divisions or subsidiaries of the company. Industry or market research reports may be helpful in finding indirect competitors. 

You can run competitor screenings in Mergent, NexisUni and Capital IQ (in the Milt Harris Library or Finance Lab).  Each have different search parameters (Capital IQ has the broadest set). You can search by geographic region, industry, headquarters, revenues (if disclosed), etc. 

For brand shares and product information, check out Passport GMID or Statista. 

For competitor data, also check industry reports, available in IBIS World, Mergent, EMIS, etc.