NameCheap is a very popular domain name registrar. If you are unhappy with your NameCheap service, these are the top alternatives for either cheaper or potentially better domain name registration.
NameSilo is one of the cheapest domain registrar. They are cheaper than NameCheap for many domains, and they provide great service. They also only focus on domain name registration. This means, that unlike NameCheap, they will never try to upsell you on their hosting packages.
Gandi is a respected French registrar. They tend to be more pricey than NameCheap, but do offer high quality service.
Finally, if you are looking for the absolute cheapest domain name possible, the registrar you choose will depend on what top level domain you want (.com, .org, etc.). Check out our domain name comparison tool to find exactly how you get get the cheapest domain name.