Obviously, you can't use the same name as another BIG, recognizable company. And you also want to avoid trademark issues.
But what about these two scenarios:
You finally find a domain name and app name that works, but after some googling, you come across another app using the same name. This other app is not well-known, and in a completely different niche. Perhaps a different platform too (they're an Android app, I'm a web-app). Will using the same name come back to bite me later?
Or this scenario: Found a good domain name and app idea name. Some googling brought up another company (not an app) with the same name. For example, I want to use sunshineapp.com but came across a company with the legal name Sunshine, Inc. Should this stop me?