The brilliant, but long-unrecognised, 20th century British scientist's name was selected with the help of a public competition in which nearly 36,000 took part.
"Just as Rosalind Franklin overcame many obstacles during her career, I hope 'Rosalind the Rover' will successfully persevere in this exciting adventure, inspiring generations of female scientists and engineers to come," said Skidmore.
She died of cancer at the age of 37 in 1958.
The three men who were awarded the Nobel Prize for their work on DNA four years later did not mention Franklin in their acceptance speeches. Franklin's contribution to their research remained largely overlooked in science books until the 1990s.
It follows in the tracks of three similar missions conducted by the United States.
"Can we find primitive life on the Red Planet?" he asked.
The new rover will try to answer that question by drilling two metres into the hot planet's surface to sample and analyse the soil.
It will use solar power to drive around with the help of optic sensors.
Scientists said it will have a degree of "intelligence" that allows it to make some rudimentary decisions on its own.
The rover will first undergo a series of stern tests to make sure it can survive extreme temperatures and vibrations endured in a journey that takes it more than 55 million kilometres from Earth.
UK engineers finished building the European space explorer at a delicate political time.
Britain is due to end its 46-year involvement in the European Union at the end of March.
Relations between the two sides are strained and cooperation on major projects such as space exploration is under review.
Britain has already been kicked of the EU's Galileo satellite navigation system because of Brexit.
The rover was built by the British-based defence and space unit of the pan-European Airbus corporation.
Its high-resolution 3D camera was built by University College London's space science lab.
"This is a big moment for British science," science minister Skidmore said.
"Although we are leaving the European union, we are not leaving ESA.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)