In order to get to the local web server we usually use http://localhost. How can I directly refer to my computer? I though puting the ip number for example: "http://38.703.837.83" would work but it didn't.
If you have Dynamic IP address you should use Dynamic IP addresses! I'd recommend you to try No-Ip for that. You have many tutorials over internet and you should google them!
I don't want to do something fancy such as running a website on my computer or accessing from somewhere else. I just want to know if the "localhost" can be replaced by my computer IP or computer name or whatever.
Within your local network, local ip, local hostname, 127.0.0.1 or localhost addresses will work. But if your external IP is called and you're using a router, then port has to be forwarded to the local ip.