During the course of litigation, you will have to refer to the parties, in letters, written submissions and so on.
There are basically two ways of doing this. You can call them by their names: ‘Mr Smith sued Mr Jones’. Or you can call them by their titles: ‘The Claimant sued the Respondent’ or sometimes ‘Claimant sued Respondent’.
It doesn’t really matter which you pick. People have different styles and most of us switch between them depending on what we’re doing (although I tend to remain consistent within a document to avoid confusion).
I have seen people write ‘C’ for Claimant and ‘R’ for Respondent. This is a bad idea, just because it looks slightly odd and the single initial tends to interrupt the flow.
Never consistently call your client ‘Mr Smith’ while referring to his employer as ‘the Respondent’. This is a hoary old trick aimed at making Mr Smith seem human and sympathetic, while depersonalising the Respondent. It is so ancient and so well known that, far from being moved to sympathy, the tribunal will be insulted by the fact that you’re taking them for rubes.