You can use one of the dynamic DNS services. I like
www.dyndns.com. They have a level of service that is free as well as more advanced levels of service that are available for a fee. They also have a dynamic DNS client software for Linux that will keep your dynamic DNS record up to date when your ISP changes your public IP address. You can then connect to your home LAN by using your dynamic DNS name. It is possible that your router already has a dynamic DNS client software built into it so you would not have to run the client software on your Linux machine.