Copyright Alliance has a comprehensive guide here but in this case you can skip a lot of those steps since you know that your works are in the data set and the website that the data set is hosted on.
The next steps are then to fill out a takedown notice and email it to huggingface. Interestingly, huggingface actually has a form template for takedown notices, which you can find on their Content Policy page - look in the 'IP Infringement and DMCA takedown process' section and you'll find it right next to the email they ask you to send it to.
Since there's space for you to list multiple works you actually only need to fill out the form once. It'll be tricky trying to fit 150 fics in there though, so you could just use a representative sample. I did that, but also copied their template into my word processor and listed all 396 of my works which are in the data set - including five original works. I then converted that to PDF and emailed both letter and form to the huggingface email.
Since you have a relatively large number of fics to list, you might also find the process I used for that to be helpful.
Step 1: Go to your list of 'works' on AO3
Step 2: Hit the 'Edit Works' button
Step 4: Past the whole lot into a word processing file and do some basic editing. The start of my list looked like this:
As you can see, the spaces at the beginning of each line make it pretty obvious which lines are titles and which lines are fandom names, so take out all the fandom names.
Step 5: Remove all the duplicates created by having crossover works - if you have none of those, then skip this step.
Because I had a lot, I used a spreadsheet program and followed the steps here.
Step 6: This should be your final list so copy it back into the form template / your letter and you should be good to go.
In answer to your other questions, there's unfortunately no way to file a takedown notice without your legal name. The good parts are that the process is the same no matter where in the world you are and you don't need a lawyer to do it, so no legal fees.
Good luck and feel free to DM me if you have problems with any of this!
