There used to be a service called Compete. You could go there and type the name of the company and get a list of similar companies. Some of them were competitors to the original company. It was not an entirely accurate list, but got a few useful companies.
When Compete shutdown, I started using Google. Type the company name + competitors in your search query. While not guaranteed, you will certainly get some useful information.
I wondered what it takes to build a build a tool that will find alternative companies. One way to do it is to look at the power terms in the company description (terms that are strongly aligned with the company tag line) and do searches to find other similar companies.
This can be a good MicroApp. I am working on it and will publish one soon.