I would advise you to put this case in the hands of your local Police, as these threats may in themself be a Criminal Offence. You should also notify the telephone company, as this individual is by this action, is also in breach of their telephone service contract.
In the US, there are a number of phone listing sites, that permit searches to be made using a telephone number.
These are not, however, permitted in the UK, as a direct result of the Data Protection Act 1998. Although the Police can request disclosure of this information, as part of their investigations. It's only if or when a case goes before the courts, that the private citizen can discover who the culprit is. Unfortunately that is a very rare event.