I'm starting a business and I'm looking into purchasing a domain name for my business but the problem I see is that another company in the UK (United Kingdom) owns the exact name of my business but in ".co", and I'm looking to purchase the ".com" which is actually available to purchase. Will this be a problem when people search for my company name?
Yes, but the problem lies not in the technical part of which site shows up. The real liability lies in whether the domain name is trademarked. You run the risk of lawsuits.