If you own a Swisscom Internet-Box (i think 2 or 3) you'll get a free and up-to-date DynDNS. You can set this directly in your Internet-Box-Interface at http://internetbox or http://192.168.1.1 (if you haven't changed anything on the IP-Config).
The URL contains a personal Subdomain (e.g. "domip") and the Base-Domain "internet-box.ch". So you can set your own Subdomain up to get e.g. https://davidswb.internet-box.ch ;-).
Please take note, that you'll have to setup HTTPS/SSL directly on the client. This is not a Domain-Based thing. I would suggest you, not to open the Webinterface to the public using this DynDNS-Service.
A normal DynDNS with a custom domain is not a part of the portfolio of Swisscom (yet). I personally use the DynDNS-Service from Infomaniak, which provides a easy-to-use Portal for creating new Subdomains. Please take note, that these Services (or other Services not from "internet-box.ch") need to be updated regularly. This because your Internet-Box does not have a permanently fixed IP-Adress.