Don't expect the domain to be 'yours' if you receive it for free or extremely low cost from your host as a part of your hosting package. Think about it, if your paying $3.95 a month for your domain and hosting and a domain registration at a the registrar's price is around $5 per year (the host is paying more for the registration) your not even paying for the cost of the domain in the first month. Maybe $0.50 per month goes toward the domain cost, so at the end of the year it's paid.

How much would it cost to register the domain from that host without a hosting plan?