IndieWeb

The IndieWeb is a community of independent and personal websites based on the principles of: owning your domain and using it as your primary online identity, publishing on your own site first (optionally elsewhere), and owning your content.

Want to get started on the IndieWeb? See:

IndieAuth - to authenticate with your website
Webmention - to notify other websites, for peer-to-peer comments, likes, and other responses
Micropub - to publish to your site using a variety of clients
WebSub - to get real time updates on other sites' new content
Microsub - (experimental) to follow others, collect posts, read, and interact with them

2024-01-26 Tantek Çelik: The #IndieWeb is for everyone…
The #IndieWeb is for everyone, everyone who wants to be part of the world-wide-web of interconnected people. The social internet of people, a network of networks of people, connected peer-to-peer in human-scale groups, communities of locality and affinity.
…
The IndieWeb is for everyone, everyone who wants independence from organizations, independence of agency to associate, and who embraces the web of humans that want to interconnect, to communicate, to value and respect each other, whether one degree apart or thirty.
2024-01-27 capjamesg: The indie web, in which he says "To have a personal website is, presently, an act of rebellion. It is a statement." Later in the post, James notes "The web is yours. You can put up a website where you share whatever it is that you want to share with others."

have more than one such personal domain.
use your own domain for purely a professional identity facet, preferring to keep anything personal off the internet/web. That's totally fine.

You own your own domain but use Tumblr.com or WordPress.com or some other hosted content solution to publish content (like posts) on your site. You own your permalinks so you can change hosting and (with some work) keep your permalinks working.
You use a full-service web site hosting service and have them maintain a WordPress or other CMS install and databases for you.
You use a web hosting service and maintain your own WordPress or other CMS project install, backup your content (files and/or databases) etc.

Just having a subdomain on a content hosting site, e.g. person1.blogger.com, person2.wordpress.com, etc. They still own your profile and your permalinks.
Just having a profile page on a content hosting silo, e.g. twitter.com/person1 flickr.com/person2
In both cases you're still subject to their policies on names and they could trivially give your name/identity away, e.g. as what happened with danah boyd and zephoria.tumblr.com (recovered only after public outcry), or the Tower Bridge on twitter.com/towerbridge (involuntarily re-assigned without notice).

See Also