This is really a DNS question but there are two possible ways. The first is as you alluded to - get a static IP address from your ISP and/or get web account with a static IP address. You can have many names on this single IP address but the IP address will not change periodically.
If your ISP is like most you have a DHCP assigned address meaning that it can change periodically. If you want to map a name to this changing address, you will need something that updates a DNS server somewhere with your current IP address. I found this information to help when searching Google for "dynamic dns".
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