Here are a couple things you should have available for possible readers or even fellow authors:
At the minimum, you should have something brief under the "intro" section, which shows up on the top left of your profile. Example: Mine says "Horror and fantasy short story author. Fan of all things creepy." It conveys what I do and what I'm interested in. No mysteries here!
You can also update your job on the "About" page, and you should link to any other social media you want people to see, such as your blog and/or website. I have links to my website, Facebook, Twitter, Instagram, Google+, and Pinterest.
Consider making some of your posts public. If that's something you prefer to avoid, pick a couple that you feel will be representative of you (book release posts or updates on writing or anything random about writing) and just make those public. This means someone checking your page will see you're a writer/author.
Have cover images, author photos, etc.? It's a good idea to have those visible to the public, as well, either in your cover photo, profile photo, or visible on your timeline.
This is where you really must have some personal information, and there are plenty of places to do it. It should be clear on the front page somewhere who you are. If your name is not in the title, be sure it's visible on the front page. Write a visible bio that includes any pertinent writing details. Make sure there is a visible way to find any books you may have out. Mine are listed along the side of my blog, as well as in a publications tab.
It's a good idea to have a few types of tabs with information. For instance, I have an about me with some random facts and pictures, a publications tab that lists all my available publications and where to buy them, a media kit tab where information about me can easily be grabbed (long bio, short bio, my social media links, headshots, and how to contact me), and an appearances tab so people know where I'll be signing and/or speaking. All of these hopefully make me more accessible and save people some legwork.
See the IWSG blog for a brief post about GDPR that includes information on how the IWSG is dealing with it and a few links I found helpful in getting the IWSG newsletter GDPR compliant.
Have you maximized your social media? Do you have information that's readily accessible for those searching you out? Have you gotten your page and newsletter updated to be GDPR-compliant?
May you find your Muse.