Vulcan has taken more than 100,000 of some 325,000 votes cast in the online poll.
A new 20-30km wide moon of Pluto currently known as P4, was discovered in 2011; another of similar size – P5 – was spotted last year.
The organisers accepted Vulcan, but rejected Romulus. Both Romulus and Remus (the names of twin brothers in the Roman foundation myth) are already in use as names for the moons of the asteroid 87 Silvia.
However, Mr Shatner appeared pleased that Vulcan made the list, tweeting: “I think we are over 100k votes for Vulcan on PlutoRocks.com that’s wonderful!”
The poll is being run by the Seti Institute in California and Dr Mark Showalter, who led the scientific team behind the discovery of P4 and P5.
The team have said they would take the results of the vote into account when they propose their choices to the International Astronomical Union (IAU). However, the IAU has the final say on the matter.
Pluto has five moons, three of which already have names. They are: Charon, Hydra and Nix.
Pluto itself was demoted from full planet status following a vote at an IAU meeting in Prague in 2006.