They still use the Hoshino surname, but they would be in the Saito Family Registry instead of the Hoshino Family Registry now. That said, we don't actually know if Ai was also in the Saito Family Registry as she was abandoned and Ichigo was her official guardian already. I don't believe the public knew Ai's surname, or if they did, it wouldn't matter.
Their family name all has the same Kanji and reading. Ai's stage name was the same katakana as her real name. Aqua and Ruby have Kanji real names and katakana stage names and neither includes their surname.
Japanese laws aren't just strict. Even if something is TRUE, but damaging to someone's reputation, they can sue for damages. In the US, libel (printed slander) is only awarded if lawyers can prove the journalist/author knew what they printed (or said) was false. If it was true, libel/slander laws do not apply.
But Aqua, Ruby, and Miyako are currently hiding that the twins are Ai's children. No one knows Ai had children except for the senior staff of Ichigo Productions, the dead murderer, and the twins' father. Possibly not even the police.