Systems similar to this exist. They’re not (all?) anonymous, however.
Every Swedish citizen and resident has a unique and dedicated number (date of birth followed by four digits), and you can use it in tandem with for example BankID (https://en.wikipedia.org/wiki/BankID) to authenticate yourself almost everywhere.
It would be extraordinarily hard to make up UBI claims for non-existing family members and receive payouts in Sweden. You would first have to convince the tax agency to register the fake person in order to get a new personal number, either as a newborn or immigrant, which either way is obviously subject to controls. You’d then have to keep this up through various mandatory interactions with government agencies without getting found out. It would probably be much more effort (not to mention stress) than just working for the same money.