Is there such a thing as online anonymity? Not really - wherever there is a directory whether or not an individual knows of it, there will be an entry. Nobody is truly anonymous any more. Everybody will have at least one public record online and visible to all. The challenge is in regaining anonymity after an identity has been published. There are various websites that claim 10 steps, 12 steps etc to anonymity but they don't go far enough. There is absolutely no way to erase all online listings of an individual nor of a former business. That is perhaps the answer sought.
When it becomes hard to erase out of date data, it becomes easier to hide in the old data. Simply ceasing to post messages online and removing social media accounts means that after 6 months or a year, all old postings will just fade away into the background of general noise.
Generally, if a nom-de-plume can be used instead of a real name, that helps tremendously. Many are not fast enough on their feet to consider a nom-de-plume. It does help though if somebody does an online search in that the search doesn't throw up anything bar former telephone numbers.
Domain names are a telltale trace of who somebody is. This is why generally, subdomains are very much preferred. Either that or an anonymised domain name (which costs extra). With a subdomain there is no record of the website/blog owner's identity.
There have been moves around the world to make blog posters and website owners more accountable and identifiable. This is a double-edged sword - it means that more responsible postings are more likely to be placed online. It also means that people will be judged by what they write which might well not be nothing to do with their ability to do a job.
On a personal level, there is somebody else with the same name as myself, posting some pretty uncouth things online. While I've not seen any of the 3 or 4 Facebook accounts operated under the same name, their Twitter account is pretty appalling in its vulgarity. There is nothing I can possibly do about this other than legally changing my own name.