Must be registered in the US, as, in the UK, this would be, for the time being, unlawful, I think.
https://www.bbc.co.uk/news/uk-england-kent-52471697
I'd be more inclined to take Greer's complaint seriously if it hadn't then verged into the "all-male families are bad" territory, rather than stuck to "the function of a birth certificate is to record biological parentage, where possible". I suspect most people would understand if the surrogate/egg donor wished to retain their anonymity, so it's right that their names aren't on the certificate, and (probably) wholly wrong of Greer to be upset on their behalf.