Is there somewhere where I can control privacy settings?

Yes. Click your profile icon in the top right, go to Settings, then the Visibility tab. 

There you control, field by field, what other members see and what partner companies see. Each field has its own switch for each audience: Skills, Experience, Education, Achievements, Projects, Contact Info, Goals, and Location.

Two more controls live on the same page:

Partner activity. Off by default. Turning it on lets partner companies see when you view or favorite their page. Partners never see your name unless you switch this on, and even then only if they have signed a data processing agreement with RTC.

Hide my profile from partner recruiters. Keeps your profile out of candidate search, resume books, and anything a partner company downloads to review candidates. It does not affect job applications you submit yourself.

Settings also holds your Notifications, Email subscriptions, and Job preferences.