Is it possible to have a custom metric in "private" mode, i.e. not visible to other users?

Yes, it is possible not to share a metric with other users of the solution.

To do this, when creating a custom metric, simply leave the visibility parameter to "Private" as in the example below:

IMPORTANT: If you choose to make your metric public, it will be available to the entire organization, it is not possible to share a metric with only certain users.