ATC in my experience nearly always has the callsigns on the screen or strips. The only exception is a new call unannounced and the first thing the ATC does is to write it down either electronically or on an official record.
Not completely true anymore, EFPS (electronic strip system used in some UK towers) does not have the callsign below the ID. Unfortunately, you just have to memorise them.
Only advice can give to memorise is to pick easy ones to remember for an interview, i.e EZY = Easyjet RYN = Ryannair TOM = Thomson etc. of course you will probably be expected to know BAW = Speedbird.