According to the official results of the Richmond-Park by-election, 2016, Goldsmith and Syms are Independent whereas Powell is not labelled at all. My assumption was that anybody who is not registered on behalf of a recognised political party would be labelled as Independent. What determines the difference between independent and having no label at all?
If you want to stand as a candidate in the UK parliamentary election or by-election as an independent candidate and you want the word independent to appear on the ballot paper, you are required to state this on the nomination form. If you leave this part of the form blank, your name will appear as unlabelled (without anything).
1.8 The following is optional:
A description – if you want the word ‘Independent’, and/or ‘Annibynnol’ in Wales, to appear on the ballot paper underneath your name, you need to state this on the nomination form. No other descriptions are allowed for candidates who are not standing on behalf of a registered political party. Alternatively, you may choose not to have a description at all by leaving this part of the form blank.
[UK Parliamentary general election: Guidance for candidates and agents]