Sometimes, due to the requirements of the training we are delivering, it is necessary that participants cannot see who else is enrolled in the same course. Is it possible to restrict this action?

Yes, usually we disable the privilege that allows the student role to view the "Participants" section. At the course level, we would remove the privilege for users we do not want to see that list.

Click on Course Administration > Users > Permissions and filter the privileges by typing viewparticipants (view participants)

For the 'View participants' capability, remove the student role by clicking the trash can next to the role name and confirm.