As far as I'm aware there isn't any setting for it etc (there is one if you want to allow the user to upload an image rather than just have the default image - to do that that you set Profile/ShowImage to true).
Without any setting then via CSS or JavaScript/JQuery (under the Advanced tab on the Web Pages Localized Content).
Edit: alternatively, if you do not want any of the existing profile links and buttons (or other functionality) you can create your own Profile Page from scratch e.g. use a standard Page Template and Basic Form (e.g. readonly).
Use the Portal/Power Pages Management App:
- Create the new Web Page and add the Basic Form you want to display the user details (use a standard Page Template such as Full Page)
- Edit the Web Link Set named "Profile", under Links tab edit the existing Profile entry to use your new profile page (this will change the nav bar Profile menu link)
- Edit the Site Marker named "Profile" to use your new profile page (this will take users who try to )
- Create a Redirect name it what you want, set Inbound Url to Profile, set Web Page to your new profile Web Page
- Clear the Portal Cache (Designer, sync then preview, or manually <yoursiteurl>/_services/about when logged in as a portal user with the Administrators web role)
after you have tested and are happy with it you will want to disable or remove the out of the box profile page as technically its url will still be active.
