The actor became a father last month when Chinese actress Tinglan Hong gave birth following a "fleeting affair" with the star and it has now been revealed Hugh and Tinglan - who is living in a £1.1 million London house bought by the 51-year-old actor`s cousin - have chosen the name Jessica for their child.
Hugh was spotted in the city this week visiting his child but neighbours of Tinglan in the exclusive London area of Fulham where she is residing said they didn`t even realise the actress had a baby.
One resident told the Daily Express newspaper: "We didn`t even know she had a child. I`ve never seen her take it out to the park, which is only a minute`s walk from here."
Meanwhile, German-born jazz singer Elisa Schmidt has denied she is dating Hugh - who is 30 years her senior - after the pair were reportedly spotted "flirting and sharing hot kisses" in the back of a taxi during a recent date.
She wrote on her band Schmidt`s Facebook page: "This is all Nonsense.We only had Dinner!That`s all... (sic)"