Clear item with custom name?

The syntax for clear is as following:

/clear [player] [item] [data] [maxCount] [dataTag]

Your command is as following:

/clear @a torch 1 1 {display:{Name:"Special Torch"}}

You are trying to clear (for everyone in the server) torches with a data value of 1, a max count of 1 and a name of "Special Torch".

Seeing as there are no torches with a data value of 1, try using the following:

/clear @a torch 0 1 {display:{Name:"Special Torch"}}

The accepted answer is now outdated. Please read this answer if you are playing in 1.13+.

1.13+ Update

The syntax of the clear command changed in version 1.13; the NBT data is now incorporated into the item parameter, the data value has been removed, and JSON formatting has been added to the Name The updated command would now be the following:

/clear @a minecraft:torch{display:{Name:'{"text":"Special Torch"}'}} 1

You can omit the count (last parameter) to clear all items that match.