'Compatible' is the wrong context for your question. DNS is common internet standard, and compatibility with hardware or firmware or with an ISP is out of scope. Every router and ISP should be able to handle DNS traffic, else it cannot really be used at all.
Regarding a router there are exactly two possibilities: Either you can manually configure DNS server addresses or you cannot. That's all. As you didn't say what exact router model you are referring to, I only can point you at other related threads: https://support.opendns.com/hc/en-us/search?utf8=%E2%9C%93&query=century+link
Regarding your ISP, you can test if you can use a 3rd party DNS service like OpenDNS with this command:
nslookup -type=txt debug.opendns.com. 18.104.22.168
How do I configure a centurylink C4000BG modem/router to block websites?
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