I switched to
no-ip.com after DYN discontinued their free DDNS. No-Ip.com is free for their basic service. I use it for remote access to all my webcams and routers. If you install their tool on one of your computers on your network it will keep the IP for your hostname up to date.
By the way, if you leave your router on you should keep your IP. Even if you turn it off and on you should still have a "lease" on that IP. I'm not sure why the OP keeps getting a different IP every day. I don't have a static IP at home but my router has had the same IP for a year or more. The last time it changed is when I replaced my router.
Dial-up is different. You'll get a different IP every time you connect.