It was chosen "in order to avoid media attention" until the company was "up and running", according to a source "with knowledge" of its formation, the Daily Mail reports.
The paper claims that the firm has filed paperwork since its inception, including a recent set of accounts - which show no trading activity - to Companies House earlier this week.
But the firm does not appear to have ever generated income or spent money, with its official status listed as "dormant". Buckingham Palace declined to comment on the claims.
The Duke has never publicly spoken about Naples Gold Ltd, meaning there has been no official scrutiny of its conduct.
He has faced previous accusations of using the same pseudonym to become involved with other companies in the past.
It was revealed earlier this month by the Mail On Sunday that Andrew Inverness had a 40 per cent holding in Inverness Asset Management (IAM), a company set up with David Rowland, a wealthy British property developer.
The company's "contacts", which reportedly included royal families and heads of state, were allegedly targeted as potential investors for another investment fund, to be based in the Cayman Islands.
IAM remained active until March this year, with a liquidator spokesperson saying they understood that the listed "Andrew Inverness" was the Queen's second son.
The revelations come as The Duke faces a number of allegations involving his business dealings, including a claim that he passed a confidential government document to a close friend and business associate.
He announced that he would withdraw from public duties "for the foreseeable future" on November 20, following the fallout from a disastrous Newsnight interview about his former friendship with disgraced financier Jeffery Epstein.