Your external IP is dynamic because the ISP can rotate it. You want to reach your home's external IP to VPN in. One common way is to create a public DNS record that's dynamically updated (by a cronjob or whatever) to always contain whatever IP your ISP last handed you.

How do you connect your VPN with your phone when you travel on the road?

Really?

Imagine, if you will, the following scenario: I have a wireguard endpoint on my home router. The home router uses a residential ISP connection and I don't want to pay $10/mo for a static IP because my ISP is cheeky and expensive. I want to have my phone connect to said wireguard endpoint to establish a secure link. I don't want to have to change my wireguard configuration on my phone every time my home IP changes.

So, I set my phone to peer with the wireguard endpoint on `home.denk.moon:1234`. Every time my home router's external IP changes, it sends a dynamic DNS update to my DNS server such that `home.denk.moon` reflects the new IP for my router. Now, whenever my phone attempts to connect to wireguard, it will resolve that domain name, get the latest IP for my router, and connect.