Are there any elements on the periodic table named after planets?

Yes: uranium.

"The 1789 discovery of uranium in the mineral pitchblende is credited to Martin Heinrich Klaproth, who named the new element after the planet Uranus." https://en.wikipedia.org/wiki/Uranium

I believe Mercury is as well. https://en.wikipedia.org/wiki/Mercury_(element)#History

Sorry, a couple more -- uranium isn't the only one.

Uranium is element 92.

Element 93 is named after Neptune: "Neptunium (named for the planet Neptune, the next planet out from Uranus, after which uranium was named) was first discovered by Edwin McMillan and Philip H. Abelson in 1940 in Berkeley, California." https://en.wikipedia.org/wiki/Neptunium

Element 94 is named after Pluto: "McMillan named the new element after Pluto" https://en.wikipedia.org/wiki/Plutonium

Element 80 (Mercury) is named after the Roman god; the planet Mercury is also named after the Roman god. https://en.wikipedia.org/wiki/Mercury_(element)#History

Element 52 (Tellurium) is named after the Earth: "Tellurium (Latin tellus meaning "earth") was discovered in the 18th century" https://en.wikipedia.org/wiki/Tellurium

There are also two more named after celestial bodies that are not planets.

Element 2 (Helium) is named for the Sun: "Lockyer and English chemist Edward Frankland named the element with the Greek word for the Sun, ἥλιος (helios)" https://en.wikipedia.org/wiki/Helium#History

Element 34 (Selenium) is named for the Moon: "Selenium (Greek σελήνη selene meaning "Moon")" https://en.wikipedia.org/wiki/Selenium

These planets were named after Roman gods - so are the elements named after the planets or after the gods?

Mercury
Neptune
Pluto