Google Maps increasingly thrives on user contributions to fill in details, but you haven't had the option to manage your public profile from the phone app you're probably using to make those contributions. That's a bit backwards, but Google is thankfully setting things right. An updated version of the Android app lets you manage your profile from a new "your profile" item in the side menu. You can make simple tweaks to your name, photo or bio, but you also get a fast track to special privacy controls in settings. Maps allows you to hide your contributions on your profile, and can opt you out of sharing your profile with the businesses you follow.
This is a remotely pushed change, so merely having the latest app release won't guarantee that you'll get it. There's also no mention of when iOS users will have this option (it's not visible there as of this writing). Whenever this arrives, it might just give you more reasons to share reviews and photos instead of keeping info to yourself.