Point dynamic IP address to domain automatically
The dynamic IP aspect of your question can be addressed easily, as there are many providers that offer Dynamic DNS as a service. For example:
- DynDNS
- No-IP
- ...as well as many others
I've tried both DynDNS and no-ip myself, and they work as advertised. This was quite a while back, but I'm guessing they're still good.
SSL certificates are based on the domain, and not the IP, so provided that your server is set up properly, there's no issue.
Although there is already an answer marked correct, I'm going to add another with more detail. There is nothing wrong with @Jarmund's answer but I think more can be said.
As mentioned, you need a dynamic DNS service. I'm not sure any of them have a "good" completely free plans anymore. Last time I had one of the providers mentioned above you were required to click a link in an email every month to "refresh" or "keep active" the free account. Needless to say the email contained advertising which despite having a filter to flag the email as important for me, often had it end up in spam instead.
That said, some router brands these day DO include a free lifetime of the router subscription to a dynamic DNS service. For example, netgear has a myNetgear dynamic DNS service offered that is powered by no-ip.com. It no additional charge after you own the router, and after setup the router itself updates the external DNS. Other router brands seem to also have this, I won't mention other names because this is the only current first hand experience I have.
If you don't have a router that supports dynamic DNS then you will need to run a client on one of your local computers that is up 24/7 to keep the dynamic DNS service up to date. This is likely the case if you are running a modem/router supplied by your service provider. You might want to look into separating your modem and router and owning your own router. Without knowing your ISP its impossible to provide specific info.
Of course, the free service that comes with a router is to a single sub-domain of a common to the service domain. Examples: MyExample.someDynamicDNSExample.com points to your local external IP.
How does that help you if you have 5 (or any number) custom domain names? The dynamic DNS service would love it of you would pay them for more, and perhaps in a few cases there might be reason to do that, but in most cases you won't need to.
When your existing shared host sets up DNS or tells you what to enter in external DNS they are likely creating or telling you to create A-records.. that is records that point a domain (or sub-domain) name to a specific IP address. In this case what you will want to do with your custom domain names is enter CNAME records (delete any existing A-records, they will conflict) with the "value" set to your dynamic serives host name, or in the example here we would use MyExample.someDynamicDNSExample.com What this is basically saying is "this domain name uses the same numeric IP as MyExample.someDynamicDNSExample.com"