The best option would be to have a DynDNS client on your phone (which your server can check) for what you want.
However, the reason VPN exists and is popular is because it works with the required security. Trusting an IP address alone leaves yourself open to abuse from another user at your ISP, your ISP, or even simply someone sending you a link to a specially crafted webpage which contains some HTTP requests, etc.
Ironically, allowing the phone to send it's IP address to your home server opens up the whole network to abuse, as the update would need to be allowed from an IP address that's not already known.
There's a reason we don't use security by obscurity.
The best option would be to have a DynDNS client on your phone (which your server can check) for what you want.
However, the reason VPN exists and is popular is because it works with the required security. Trusting an IP address alone leaves yourself open to abuse from another user at your ISP, your ISP, or even simply someone sending you a link to a specially crafted webpage which contains some HTTP requests, etc.
Ironically, allowing the phone to send it's IP address to your home server opens up the whole network to abuse, as the update would need to be allowed from an IP address that's not already known.
There's a reason we don't use security by obscurity.