Doesn’t addition of the word ‘independent’ make it a distinct name?
Yes and no.
It does for everyday purposes but not for UK electoral law where the issue is what name can be put on the ballot paper.
The UK Electoral Commission is pretty strict on party names and variants of them so as to avoid confusing voters. For instance, they refused to allow the Trotskyist “Socialist Party of England and Wakes” (SPEW) to register under that name as they held that would confuse voters with us. The SPEWers are however free to use that name on their election literature but on the ballot paper they appear under their registered name of “Socialist Alternative”. Just as the new ISPGB would be free to.
On the other hand, the Commission has just given us notice that they intend to strike off one of the registered variants of our name — The World Socialist Party (UK) — on the grounds that this doesn’t identify who we are to voters. We have appealed and are awaiting their final decision.
Incidentally, there is a suggestion that this new party might be a rightwing outfit rather than yet another “socialist” party. See the discussion here.