It depends on the settings chosen by your organization.
By default, officials can only see who is working at games at the same location and on the same date as their own assignments. Other games will only show "Assigned" or "Unassigned" in place of the officials' names. Some organizations even choose to hide from officials the assignment status of games not assigned to the official.
Some associations choose to reveal all assignments to all officials, but some enable the ability to see the assigned officials' names when searching for games by a specific date or within a certain number of days preceding a game.
By default, schools/teams can not see the officials. There are options for an organization to reveal the officials names to the payor or to any team on a game. When the names are generally visible, the names can be hidden until the official accepts the assignment.