Do you want ads on your site?
There are two types of “free” domain names. The first is one that places ads on your site. The second locks you into a hosting plan. You don’t want either one.
But it says I get a free domain with hosting.
You need to read the fine print. In the Terms and Conditions it may say “you will receive a free domain of your choice for one year” or something similar. What happens if you think the hosting is lousy and you want to change to a different company? You can do that, but you can not continue to use the domain because you never owned it. The hosting company did.
So, you have two choices. First, you can register a new (different) domain name, which cancels everything you have done to promote it during the time you used it. You will be starting from scratch.
Your old domain name eventually becomes available for sale, usually at inflated price. Anybody can then buy it, including any competitors you may have. Now, all the work you did to boost your original domain name goes to benefit your competitors.
Another choice is continue to continue to pay for the old hosting as well as the new hosting. You won’t be using the old hosting any more, but because the “free” domain name was a part of a package, you have to keep paying because they owned the domain name, not you.
Do it the right way
Register the domain name you want with an Internet Registrar yourself. The domain name is then owned by you and you can do anything you want with it. DO NOT buy hosting from the same company. It is always good practice to keep the companies that provide hosting and registration completely separate.