The Phantom Menace is not a person, but a reference to the overall situation that the characters find themselves in throughout the movie.
Though we have several villains in the movie:
- Darth Plageous
- Darth Sidious
- Darth Maul
- The Trade Federation
- The Separatists
Menace is defined simply as
a person or thing that is likely to cause harm; a threat or danger.
Sometime during the film, but off-screen, the Clone Army is ordered:
OBI-WAN: Yes, Master. They say Master Sifo-Dyas placed the
order for a clone army at the request of the Senate almost ten years
ago. I was under the impression he was killed before that. Did the
Council ever authorize the creation of a clone army?
MACE WINDU: No. Whoever placed that order did not have the
authorization of the Jedi Council.
This answer, talking about Episode II
We know that this was done so that the Empire would have an army to use later. The use of this army must be justified, though, as it has been a long time since the Republic had a standing army. As such, the Sith must create an environment in which no one will even blink when they destroy the Republic in favor of the Empire, and adopt this army.
How does one precipitate the chain of events that need to take place to see the rise of Palpatine and the Empire? By creating fear and confusion, and manipulating those most affected by said fear and confusion into pushing events forward.
This is largely accomplished with the blockade of Naboo. This directly results in Palpatine becoming the Supreme Chancellor, as Queen Amadalla herself calls for a vote of No Confidence in the current Chancellor, an action for which Palpatine is already prepared with votes to gain the position.
Even though the main villain is definitely Palpatine, we can safely assume that The Phantom Menace is simply the menace of the situation, the origins of which are hidden from the Jedi and the Senate, as well as the galaxy at large.