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If your new paint is classed as 'custom' (which may be as simple as not being a standard colour) it may increase the cost of any repairs or alter the market value of the bike - not necessarily something you'd find in the insurance schedule, but could be used as an excuse for not paying the full amount if you make a claim.
Most brokers / insurance companies will hit you with an admin charge for altering policy details mid term, but not for changes at renewal time...
A bit of googling returns lots of people stressing how you absolutely positively must inform your insurer and how a hundred puppies will be slaughtered if you don’t but as you have, I’ve noticed that colour isn’t mentioned on my insurance docs and I don’t remember the colour being specified when I entered my reg number to bring up the bike details when I was fucking about with insurance recently.