Unhide All Designator Altium
If you right-click on any designator and select "Find Similar Objects", a window appears that allows you to select your filters. Next to "String Type" make sure it says "Designator" and the dropdown on the right is set to "same". Check the "Select Matched" and "Run Inspector" boxes at the bottom and click "OK":



This will select all designators on your board. At the same time it will start a tool called the "PCB Inspector", which allows you to change the properties of all selected components at the same time. Once in the inspector, simply uncheck the "Hide" box under the "Graphical" heading and press your enter key:



This will apply the change to all of your designators.

Alternatively, instead of right-clicking a designator, you could also right-click a component instead and select "Find Similar Objects". In the filter window just leave "Object Kind" as "Component", and again make sure the "Select Matching" and "Run Inspector" boxes are checked, and hit "OK". When the Inspector opens you can check the box labeled "Show Name" under the "Graphical" heading. This will also show all of the designators. 

The second option may be your best bet in case for some reason "Find Similar Objects" doesn't select hidden items (I can't remember if it does or not).