I'm afraid this is not possible right now. There's a related issue you might want to watch and vote for though:
While I doubt that it will ever be addressed as phrased in its title, Jean-Pierre's comment proposes the 'ability to either remove "popular" and "browse all" or to have a choice between a static or dynamic home page', so maybe you can comment with your requirements as well to shift the issue scope into this direction.
The Popular Section will only show other Service Desks that the logged in customer has access to. If a Service Desk is displaying for one of your customers that you don't want them to see, then you will want to modify your Customer Permissions in Service Desk.
For example, say you have two Service Desk Projects, and you don't want users from Company A to see Company B's Customer Portal referenced in their Popular tab.
To do this, you can go to Customer Permissions (<BASEURL>/servicedesk/admin/KEY/request-security) then you can select under Who can raise requests? > Customers who are added to the project. This way, only the customers you added under your Customers List (<BASEURL>/projects/KEY/customers) will be able to see the Customer Portal for their project under their Popular tab.
I hope this is clear!
In addition, we have a feature request to be able to hide this section as well as the Browse All:
I recommend voting on that issue to help show the need for such a feature, and please feel free to comment with your usage case on that ticket.
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