Welcome to the Ranch, Jose!
Technically, you already
did deploy it in a domain: localhost.localdomain, which exists on just about every machine that runs TCP/IP. But you want it visible on an
external domain as well.
There are a couple of things that have to be done here. First, you probably want to get rid of the ":8080" in your URL. But that's more complicated than you'd think. Doman Name Services (DNS) is a map of domain names linked with IP addresses. But 8080 is a port, and DNS doesn't keep port numbers (a domain often serves up multiple ports, depending on the service and protocol being used). So you either have to make Tomcat serve on the default port for the HTTP protocol (port 80) or you have to connect Tomcat to something that can.
Port 80 is in the "magic" range of port IDs that cannot be uses by unprivileged applications, so you have 2 options here. One is to run the Tomcat server under a priviliged account - which is a security risk, and the other is to employ what's known as a
reverse proxy server. There are quite a few servers that can safely listen on port 80 and forward to Tomcat. Among them are Apache HTTPD, Nginx, and Microsoft IIS. A Reverse Proxy is a good thing to have for a large shop, since it can serve as the target for all the shop's webapps, not just the Tomcat cones. Incidentally, people will often simply say "Proxy Server" here, but a true Proxy Server works in the opposite direction. As long as you know which way things are going, it won't matter too much.
In a proxy server, you define Virtual Hosts, and that means that we can have
https://coderanch.com,
http://www.javaranch.com and other domains all proxying for the same backend Tomcat server. The host mappings can include Context paths as well, so that we can do things like have multiple apps in a Tomcat server and proxy
https://coderanch.com to localhost:9080/javaranch and
http://www.permies.com to localhost:9080/permies. And even
http://www.getInfo.ue.com/spyInv to localhost:9080/myProjectMed. Note that the backend tunnel uses port 9080, not 8080. The tunnel protocol is different than http and https, so Tomcat has a different port for it.