This method takes a bit more time, but it works for everything and any time.
Next time you want to whisper this person again, you can just click on his name in the Buddylist.
: Go to your Buddy list.
To open your buddylist, press on the icon that has two people on it.
If you're already playing a game, then the Buddy list is located at the bottom-right corner:
: Press on Add Buddy.
: In the pop-up, enter the name that you would like to add.
For example if I want to Mayhem, I have to write his full name [GS]Mayhem.
: After adding [GS]Mayhem to your buddylist, search for his name in your list of Buddies.
Left-click on his name.
: In the black information pop-up, click on Private.
: If you have done everything correctly, your chatbox will look like this.
Everything that you type in the chatbox will automatically be whispered to [GS]Mayhem now!