* Treasury proposes Descalzi as new Eni CEO
* Starace nominated Enel CEO, Moretti slated for top Finmeccanica job
* Two women proposed to chair Eni, Enel
* Shake-up tests PM's pledge to end cronyism (Adds details of Poste Italiane CEO, background on Marcegaglia and Grieco)
By Stephen Jewkes and Danilo Masoni
MILAN, April 14 (Reuters) - Italy proposed new managers for state-backed companies such as oil major Eni and defence group Finmeccanica on Monday in a shake-up that tests Prime Minister Matteo Renzi's pledge to break with old-style cronyism.
Renzi, 39, whose campaign for change has earned him the nickname "Demolition Man," chose a combination of maverick insiders and successful private businesswomen in an attempt to prove Italy was leaving behind a tradition of dishing out jobs according to political horse-trading rather than merit.
In a statement late on Monday, the Italian treasury, which holds core stakes in some large listed companies, proposed veteran exploration head Claudio Descalzi as chief executive for Eni, replacing Paolo Scaroni after three terms in office.
For the top job at scandal-hit Finmeccanica, the government put forward Mauro Moretti, known for turning around previously loss-making state railways Ferrovie dello Stato.
Francesco Starace, currently at the helm of renewable energy group Enel Green Power, was the government's choice as the new CEO of Italy's biggest utility group Enel, stepping into the shoes of long-standing CEO Fulvio Conti.
"The government has probably listened to the market as the list of candidates, especially at Eni and Enel, is a good choice for international investors," a leading energy sector executive said on the condition of anonymity.
Emma Marcegaglia and Patrizia Grieco, two prominent businesswomen from the private sector, were proposed as chairwomen of Eni and Enel respectively, the first time women have made it to the chairmanship at the two companies.
Half of Renzi's cabinet ministers are women and the prime minister has said he wanted to boost the participation of women in the boardroom.
Italy's postal service, which is due to be partially privatised, could also have a chairwoman if the government's candidate, former European Parliament member Luisa Todini, is confirmed in the role.
Renzi said the chairman salary at state-backed companies would be capped at 238,000 euros ($328,800)a year.
All the candidates will have to be confirmed in their roles by shareholders at annual meetings due in May.
Renzi said he was "especially pleased" with the strong female contingent at top state-controlled companies. It remains to be seen whether they will be given executive powers, insiders said.
Renzi had promised to listen to the market in choosing executives at state companies, who get nominated every three years.
Veteran Eni executive Descalzi, who has helped focus Eni on lucrative resource discoveries, has been at the company since 1981 and is one of the most respected executives in the oil and gas business.
Experience also played a big role in the choice of 58-year-old Starace, a nuclear engineer by training who is also a former head of the utility's power generation business at the time Enel acquired Spanish utility Endesa.
Moretti, an outspoken executive who was seen as a possible candidate for Industry Minister in Renzi's government, will have the delicate task of turning the page at Finmeccanica after judicial scandals that have hit the defence group while it seeks to join an expected consolidation of the defence industry.
His appointment does not come without controversy. He recently drew criticism after threatening to walk away from a job paying 850,000 euros a year, complaining that the head of German rail group Deutsche Bahn earned three times his salary.
Marcegaglia, Grieco and Todini, meanwhile, have all cut their teeth at household-name Italian organisations.
Marcegaglia is co-chief executive of her family's steel group and the only woman to have been boss of Italy's main business lobby Confindustria, a role which has been filled by bastions of Italian industry including Fiat founder Giovanni Agnelli.
Grieco is president of 105 year-old computer maker Olivetti and Todini is a board member at state broadcaster RAI, as well as chairing construction company Todini, part of Salini Impregilo. (Additional reporting by Isla Binnie, Writing by Stephen Jewkes and Lisa Jucca; Editing by Janet Lawrence and David Gregorio)