@Krishan Mistry If you own the domain, you shouldn't need to upgrade anything in order to setup a custom domain for a website for almost all domain registrars. The first step is for you to determine who owns your domain if you don't remember who you selected. Sites like www.whois.net can help you figure out who the domain registrar is for your domain. Once you know who the registrar is, you'll need to remember your account information to login to their site. This will then give you the ability to edit the DNS settings, which will then allow you to add a custom domain.
Is this an outlook.com Office 365 account (think consumer/prosumer)? If so, this document here calls out that outlook.com Office 365 accounts only support GoDaddy for custom domain email. During this process you would have created an account with GoDaddy. You'll need to login to the GoDaddy site and then complete the steps I provided in the last paragraph to configure your domain with an Azure Web App.
If you aren't using the above consumer/prosumer account, are you using a business/enterprise version of Office 365? If so, according to this document, GoDaddy is again the default and you would need to knowingly pick an alternative hosting provider. You'll likely need to locate your GoDaddy account information for this type of account as well.
Are you looking to create an Azure Web App to host your web site? If so, please follow these steps once you've logged into your domain.
Please let me know if you have any further questions as you work towards this.