Let's say that there is already a niche website on the internet called:
Then if I want to register...
...but have my own/original content on it, will it affect my ranking?
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Local Rankings It may affect your rankings if its a local business name as this would effect the unstructured data (Just company name mentions, locally, or at least confuse Google a little.)
Web Rankings If your website is aimed for everyone across the globe then definitely not, Google will treat your site as a new site and not even factor in the other site - otherwise what would be the point in different domain types, i.e. .net .org .com .co? Google wouldn't go down too well with ICANN and all the other registrars if this was the case.