Among them are child molester Paul Falconer and kidnapper and rapist George Clark, who have been released from prison.
Falconer, 43, was jailed for eight years in 2006 for molesting two young girls – one aged five – in Prestonpans, East Lothian in 2004.
While in Peterhead Prison, he converted to Islam and on his release had adopted the name Mohammed Farooq.
Clark was jailed for a minimum of 12 years in 1996 after abducting a 23-year-old student in Aberdeen before driving her to his Edinburgh home and raping her.
He was freed last year after obtaining a work placement at an old people’s home and is now officially known as Yousuf Muhammed Ansari.
A Freedom of Information request revealed that police in Scotland are investigating 37 cases where sex offenders have used a legal loophole to hide their true identities.
It is easy for paedophiles to change their name. For a £40 fee they can have their birth certificates altered by changing either or both of their Christian names or surnames.
They can then register under their new identities with employers and even obtain a new passport or driving licence.
Apart from the cases known to police, many more sex offenders and criminals could be wandering the streets and it is possible that those required to report to police under their former identities could be doing so while living a double life.
In England, sex offenders are required to inform police if they change their identities but no such legislation exists north of the Border. Falconer’s ex-wife, Melanie, is said to be appalled by Falconer’s change of name. She said people should be warned about his new identity.
Children’s organisations and politicians said the Scottish loophole should be closed.
Scottish Labour justice spokesman Lewis Macdonald said: “The Scottish Government has a responsibilty to ensure that offenders deemed to pose a threat are properly monitored. If there is a loophole compromising public safety, it should be closed immediately.”
Scots Tory chief whip John Lamont said: “We have the technology to stop this happening. It is hard to imagine a situation where a sex offender changes his name for a legitimate reason.”
The National Society for the Prevention of Cruelty to Children called for the same process in England and Wales to be applied in Scotland.