Currently, there is not an option to disable by fund page without a template customization. You have the option to change the Donor Recognition Name to "Anonymous" or make a gift display adjustment on the personal campaign configuration itself. 

To change the donor recognition names to anonymous for gifts already received:
  1. Donation Management > Personal Fundraising
  2. Search for the campaign in question and select Manage.
  3. Select View/Edit next to the fund page.
  4. From the Donations List, select View/Edit next to the gift.
  5. Change the Donor Recognition Name to "Anonymous"
  6. Save your changes.

To change how many gifts must be received before they will be displayed on a fund page:
  1. Donation Management > Personal Fundraising.
  2. Search for the personal fundraising campaign and select Edt.
  3. Select Step 3. Define fee and Gift Information
  4. Under 4. Funds Raised Tally Count, enter a value which will dictate the number of gifts that must be received before the monetary amount of funds will display on a champion page. If you do not want donations to display at all, set this value to a large number. 
  5. Save your changes. 
     
If you are interested in having this adjustment made to your site's template, Contact Support and reference this article.