It makes a huge difference. The registrar owns the domain name and has the rights to sell or transfer ownership.
Let's say over the next year you invest money in marketing that domain and it becomes a money making machine for you. Then the owner of the domain name asks you for $5k to let you continue to use that domain, or $10k to sell it to you.
Or the registrar could let the domain expire and someone else could by the domain name and hold you hostage.
If you don't pay up, you have to start marketing a new domain from square one.
Always, always, always put domains in your own name. When we build a new site for someone we always have them register their own domain name.