I have a Raspberry pi. It will operate a webserver to allow the user to configure it, and will have a static IP of 192.168.0.100 (or whatever).

After they configure it via the webserver, they will place it on their network, and it needs to use a dynamic IP provided by their DNS server.

Am I able to set up a Linux device so it has both a static and dynamic IP address?

That would all depend on where in the network this device is connected. Is it connected directly to the providers network or is it sitting behind a router/switch that is connected to the providers network?

If it is connected directly to the providers network is the provider supplying more then one IP Address? If the provider is only allocating one IP then you cannot assign another on the same interface and have it work.

If connected to a device that can and does do NAT then you can configure more then one IP Address.

Yes you can use alias, but two addresses cannot be on the same subnet.

Thank you lazydog and Emerson.

An IP alias can be on the same subnet.

One method would be to create a run-first service that sets an IP address as desired. Once its configured the run-first service is disabled. I assume the Pi is configured separately from the network. Depends on what OS/version you will use to configure the Pi but DHCP clients if they can not find a server will assign an AIPIA address i.e 169.254.x.x. If you assign a static AIPIA address to the Pi then a computer directly connected to the Pi should work without configuration.

Otherwise you need to manually configure the device connected to the Pi or know the network environment. How computer literate are they?

I'm curious as to why you say that?

Well, I have tried it in past and I had some routing issues. I solved it by putting the alias on a different subnet. But then again, you may not need to route it at all if used only locally.