It's an interesting question. With my race timing hat on, I only see names as people enter them on the sign-on form (which I can't show you currently as there isn't a race to sign up for, but it asks for "Your name (as you would like it to appear in the results)" along with assorted race-class-related details. This generates an item to be purchased in the webshop, for which a (usually) card payment is made, and a more 'official' name may be given. We can fish those records out of the shop records as needed, but obviously there's the possibility of someone paying for another person's (usually a family member) race entry, in which case we'd never have an offical record of who "Tom D" or "HippyHandcyclist" might be. You don't have to be a BHPC member to enter a race.
We do collect phone numbers, originally as a Test & Trace requirement, but we've kept it up as an emergency contact method in case we turn up to discover that the venue has been double-booked or the track has been trampled by Godzilla or something, and a phone call might save people the travel.
Prior to the online entry system, we'd have had someone writing "Tom D" in a spreadsheet in exchange for 8 quid in cash.
I'm not aware of our liability insurance requiring a list of participants (I read the small print a couple of years ago, and most of it pertains to not having a bouncy castle). Indeed, an insurance claim against the organisers is as likely to be from a random member of the public who decided to ignore the signs and empty their dog on a live race track as from one of our entrants. And we routinely have non-racers trying out machines on the track between races.
We're not affiliated with British Cycling or similar, so we don't have to conform to their arbitrary rules. (Just those of the venues, which are mostly plastic-hat-related.)
