Am I able to assign DNS web URL's to my SharePoint Online site collections? Or am I limited to the tenant address?
You cannot do that in SharePoint Online.
The only things you can choose:
- TenantName. This will always look like https://TenantName.sharepoint.com/ You can choose tenant name only once you create it.
- Site collection path. Either /teams/ or /sites/
- Site collection URL. /sites/New_Site_colleciton_url
So any new site collection you create will look either like
And there is nothing you can do about it. Not in 2017 anyway.
I've heard suggestions of getting your custom domain. Even if you get your custom domain - it will only affect your user's email addresses. The tenant URL will remain the same. Yes, you can host a site on https://yourdomain and have a redirect to https://TenantName.sharepoint.com, but it will not change the URL of your site collection. And users won't be able to use https://yourdomain URL in any applications like Word, onedrive, etc.
You are limited to the provided tenant address. However, you can try buying a domain of your own,and map it to your site collection.