The ministry's work safe general manager Brett Murray replied that former Pike River general manager Doug White had indicated he would not return to New Zealand as a potential witness, but he did not object to his name being released publicly.
However, "a number'' of others indicated they did not want their names released.
"A number'' also did not even reply to the department as to whether their names could be released, so they were withheld by the ministry anyway.
The Greymouth Star has appealed to the Ombudsman the ministry's decision to withhold the rest of the names.
Pike River widow Anna Osborne said the names definitely should be released.
"I would like to know who they are.''
She also said it seemed the victims had no rights, and failing to appear was "cowardly''.
Meanwhile, the bad summer slowed the $7 million re-entry at the Pike River mine, with Solid Energy saying it expects to release an updated timetable shortly.
Helicopters have made 1300 trips and the the main ventilation shaft, pictured belching flames after the 2010 disaster, is now plugged.
Three drill holes have been done, two into the main drift and one into pit bottom.
Although they have helped inform workers, cameras lowered down have not found any surprises.
A pump will be installed to take out water, and stop it building up behind the new seal that will go in front of the large rockfall.
The next stages are to plug with foam, pump in nitrogen, re-ventilate the tunnel, then allow Mines Rescue staff to walk up to the seal. Permanent seals will also be installed, Solid Energy spokesman Bryn Somerville said.
The company hopes to update its timetable soon.
However, Mr Somerville reiterated it was important the work was done safely.
Although the summer weather was poor, Westport has just experienced its driest March on record.
- The Greymouth Star
