The free level only allows "azurewebsites.net subdomain with FTP/S and SSL".
If you want a custom domain name in Azure Websites, then you need to pay for the "shared" level (at least) and in my opinion the price goes over what any standard hosting company would charge:
I would definitely recommend this; especially if you're a developer looking to host a personal webpage for employers to look at. You can also create a page for each of your projects on GitHub!
Costs me about $0.50 a month to host a simple, static site.