Well, google search, bing search, startpage search and stuff for your name and variations of your name. Also search family members to see what you are potentially tied to with them. Search for old usernames to find anything too. Past that there are tons of Whitepage like sites that have your info and potential ties. These sites have to legally remove you if requested. There are services like DeleteMe (
https://joindeleteme.com/ which I have used) which send out mass opt-out emails to all the sites that have your information. If you don't want to pay, there usually are opt-out FAQ's associated with every site. Also, NEVER be a registered voter. Voter registries get you doxxed.
Also, a good thing to do is make sure you know exactly what is out there and that could be tied to you. So past search engines, social media search, access public records (like court records, voter records) to see what could potentially be tied to you. However, you may not be able to remove some info.
You will never be 100% anonymous and you can and will be outed if someone or something really wants to fuck you. Know what is tied to you. If you want to do something nefarious, use a logless VPN like NordVPN for online use. Use burner emails from places like protonmail or tutanota. This will make it super hard to tie you to whatever activity you are doing, but again is not 100%