Sorry if this question sounds stupid but I am new to this forum.
Do I have to install it as a subdomain (discourse.domain.com)
No, you can install directly on example.com if you wish.
Subdomains are not a requirement.
However, with hindsight a year or two down the line, you may wish you had used something like community.example.com
We are facing this issue now, as we have a desire to run a web site on our root domain and switching everything over to community.example.com after six years of only using the root, is not ideal 
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Most people today think that you should use a subdomain, so if you think you want domain.com you should use www.domain.com. In Chrome, at least, it’s difficult to tell the differences between domain.com and www.domain.com. You can redirect the bare domain to your www, using https://forcewww.com/ or a bunch of other ways.
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Are you doing a standard install, or using discourse.org hosting? In either case, going with WWW rathe than the bare domain is probably what you should do. If you’re self-hosted, it’s not hard to use the bare domain, if you’re buying hosting, it’s harder, but possible sometimes.
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