Changing call signs (or tail numbers) is fairly common from even early training. Its something that many pilots are accustomed to even before they get to the big operations.
As a student pilot its quite possible your flight school will have a few airframes usually of a given make. You may not always fly the same airframe and will get accustomed to rotating tail numbers. I did all my training in one of 3 Piper Warriors all outfitted the same.
From there many who plan to go to the airlines get their commercial ticket and instruct first to build their hours. While students will only fly a given type of airframe instructors may fly all the various makes the flight school owns. The last instructor I was flying with in any given day usually flys one of two Archers, An Arrow, one of 3 172's and a 150 all with different tail numbers.
Some pros may go on to fly 135 charts if they are lucky. Often times smaller chart outfits will have a variety of small aircraft that are constantly flying short hops and rotating crews allowing plenty of practice at hopping call signs/tail numbers
Once at the ATP level you already have a lot of hours flying a variety of planes, often all in one day.
Many smaller aircraft have a placard with the tail number affixed to the panel somewhere (like in this citation cockpit).