I've been in many situations where a developer purchases a domain name for a client, and shortly thereafter the parties split ways. The client then hires me, and now we have to go through the domain transfer process. Many times there's no friction from the jilted party, but sometimes it can be a mess.
The best way to avoid this situation altogether is to buy your own domain name. If you allow your developer to purchase your domain name, it technically belongs to them. Buying a domain is a very simple process, and there are several vendors to choose from.* I use GoDaddy for my domains, but there are several solid registrars. It's an easy process and your new developer should be able to help if needed. I have a GoDaddy Pro account, so I can set up an account at GoDaddy for my clients and invite them to enter their payment method. Once that's done, I can secure the domain and access it as needed. If they choose another developer at some point in the future, they just cancel my administrator account and move on.
*I'll write another news post soon about how to navigate the domain name buying process and what separates some domain registrars apart from others.