I think the idea of being an 'organisation' is that you can add other people within the organisation to the list of claimants. This obviously doesn't apply to a sole trader, so I'd agree with you that it probbly doesn't matter.

One way of doing it might be to use your own name and then say 'trading as....' - e.g. John Snooks trading as 'Snooko Associates' (the use of 'Associates' is often a sure sign that someone is trading on their own....).