In more normal times, most people outside of R&D would never encounter the name.
But I still maintain the official names are ridiculous. “Vaxzevria” is the trademark used by AstraZeneca in the EU. (As you say, not ChAdOx1.) And yes, the general population end up seeing Vaxzevria, on their vaccine information forms, and online at https://www.ema.europa.eu/en/medicines/human/EPAR/vaxzevria-...
For other drugs, an amazing amount of effort is devoted to finding something that a) sounds "promising" but b) without making legally-untenable promises.
The name `Viagra`, famously, is supposed to evoke ideas of vigor and Niagra (Falls). Pfizer had some trouble with Champix (varenicline), which some regulators thought was too close to "champion", and so was called Chantix in some markets instead.
I suppose you mean the vaccine names are mainly useful for regulatory purposes, because the general population will continue to name the vaccines after the manufacturer or researchers?
Why couldn't they just be called Moderna/Pfizer/... Covid Vaccine?
[1] https://www.ema.europa.eu/en/human-regulatory/overview/publi...
[2] https://web.archive.org/web/20210305190828/https://www.ema.e...