If your web host is offering a free domain with your purchase of a web hosting plan. You should read into the fine print and figure out what the exact terms are. Most web hosts do from time to time, offer a free domain with the purchase of a web hosting plan, if you are a new customer. If you take them up on the offer. Make sure to ask your web host a lot of questions thou to understand the terms of the deal. It may not be a deal if the terms are not favorable to you.
Questions to consider asking or read the fine print to figure out the answers for yourself:
1) What happens to the domain name if you cancel your web hosting plan after 3, 6, or 12 months?
2) Who would be the listed as the registrant for the domain under the whois? Will it show your email address or your web hosts email address?
3) What will the renewal cost of the domain be for next year and the year after that?
4) What happens to the domain name if your web hosting account is suspended?
5) What is the process to transfer the domain from your web host to a different domain registrar? Can you access the EPP/transfer code inside your control panel and unlock the domain yourself, or do you have to manually inquire with your web host to get the transfer code and unlock the domain?
6) How long has web host been in a business?
7) How many days does it take to change the whois information for the domain, unlock it, get transfer code, and transfer it? Some web hosts may take days to weeks so do your research!