They don't - unless you host your new domain name with the ISP.
You will be well advised to host your new domain name with a dedicated web hosting company. All web hosts will offer a Domain name registration service, and usually they'll set you up with a domain name and a starter web-hosting package at very low cost.
There are hundreds of such companies, and everyone has their favourites. To get an idea of what's involved, take a look at
click here and
You'll retain your existing ISP for internet access, but your site will be hosted elsewhere. It all works very smoothly, so no worries.