Hi,
You must first register you domain name with an ICANN accredited registrar. I searched and it doesn't appear you have done this yet:
Once your domain has been registered you can create the required dns records (asuid) to verify your custom domain for Azure App Service purposes in the domain registrar's portal. You don't need to use Azure DNS solely for this purpose. Your domain registrar will typically provide basic DNS services for no additional charge.
There are many ICANN accredited registrars to choose from. You may do a web search (search term "register domain name" to find one you like and/or search on ICANN using link below:
https://www.icann.org/en/accredited-registrars
I recommend choosing one that provides whois privacy protection at no extra charge, free email redirection, free dns service, and costs less than $15/year to renew. Some companies will try to "trick" you with ultra-low first year price and then when you renew in the future their annual price is much higher than other companies. It's okay to use one of these, just understand what the future renewal price will be so you are not surprised.
-TP