What options has Microsoft allowed for using custom URLs in Sharepoint Online? We're currently on Sharepoint 2013, and are deciding whether to use 2016 on-prem or online. We currently have 2 web apps with 2 different URLs, and we need to keep it that way.
One sentence in advance: If you ask google about this topic, you get a lot of information about a feature named "Public Site". This feature is no longer available, so all that information is invalid for today's deployments.
If you enable SharePoint on your O365 tenant, you will be assigned a URL
tenant.sharepoint.com. This cannot be change or extended right now. So think well about your tenant name! If you create new SiteCollections, you have to create a SiteCollection like https://tenant.sharepoint.com/sites/site1.
If you need more than one URL, you might have the idea to create two O365 tenants. Don't do that!
One workaround might be hosting a small site with a redirect to your SharePoint site named like mentioned above. I tested a simple CNAME some time ago, unfortunately that didn't work.