Should I run one server with multiple nameservers?

The ideal solution here is to run multiple servers rather than multiple nameservers on a single Linode. The primary thing to keep in mind when setting up multiple nameservers is the idea of redundancy. Allow me to explain:

Let's say you have two separate servers running, each with their own IP, and each one is running a nameserver. If one of the servers goes down for some reason, the other server is still running and accepting queries. The second server is now providing a failover option for the first one, thus creating a redundancy.

If you have more than one IP address on a single server trying to run more than one nameserver, there is no redundancy/failover in place.

This, plus the fact that Linode follows ARIN's IPv4 utilization criteria (which doesn't approve multiple IPs for the separation of services such as management networks), is the reason Linode won't approve multiple IPs on a single server for cases like this.

If you want to read up on this more, there is a great Community post discussion that goes into some more detail about this:

Question about private nameservers.

*Quick note: If you happen to be using cPanel, you can actually adjust your configuration so that it does not require more than one IP address to park a domain: WHM > Tweak Settings > Allow Sharing Nameserver IPs.

Finally, here are a couple more resources that might help point you in the right direction:

Via StackExchange: When are multiple nameservers used?

Via Linode Docs: Use One Domain on Multiple Servers