Most likely the MIDI file has the notes of both parts combined onto a single channel. I'm not very familiar with all of the options available for displaying scores on a Yamaha keyboard, as none of the models I own include that feature. But the only way to keep the left-hand part and the right-hand part separate from each other is to put them on separate channels. That's most likely something you would need to change within the MIDI file itself:
(1) Copy the data of the original MIDI channel to a second channel, so both channels contain the same data.
(2) Delete selected notes from each channel-- that is, delete the left-hand notes from the channel you want to be the right-hand channel, and delete the right-hand notes from the channel you want to be the left-hand channel.
You can use either a DAW or musical notation software to do this.
The first part is easy, but the second part can be more complicated, since the left-hand part and the right-hand part might not be strictly limited to specific ranges of notes.
For instance, the simplest approach is to divide the two parts at Middle C, such that the right-hand part contains Middle C and all the notes above Middle C, and the left-hand part contains all the notes below Middle C.
But sometimes the right-hand part of a piece of written music will extend below Middle C. Usually they would be shown as part of the treble clef staff using ledger lines below the staff. But if the right-hand part extends far enough into what would normally be the bass clef staff, the notes might be written with an octave indicator-- that is, written one or more octaves higher than they're meant to be played so they can be placed within the treble clef staff, but with a bracket and ottava symbol above or below the notes to indicate that they're to be played one or two octaves higher ("8va" or "15ma"), or one or two octaves lower ("8vb" or "15mb"), than they're written.
The same can be true with the left-hand part-- the notes may extend above Middle C.
In other cases, rather than using the ottava notation, the music will be written with an actual change of clef-- that is, the staff will begin with a treble clef for the right-hand part, but partway through the music a bass clef will be drawn on the treble clef staff, indicating that the notes which follow are to be played as though they were written on a bass clef staff; and then the treble clef will be given at the end of that passage to indicate that the notes are to resume being read as normal for the treble clef staff.
Similarly, the bass clef staff may suddenly change to a treble clef staff for a time, before changing back to a bass clef staff.
And in some instances-- such as when the keyboardist is supposed to play a run of notes which starts at one end of the keyboard and procedes to the other end of the keyboard, alternating between using the left hand and the right hand-- the notes might be written as normal on the grand staff but with brackets above or below the notes indicating that specific groups of notes are meant to be played with either the left hand or right hand for the greatest ease.
A variation of this would be where the keyboardist is supposed to keep playing a left-hand or right-hand part normally, but reach across with the other hand and play some additional notes for a bit-- that is, play with the hands crossed temporarily.
Anyway, after you copy the original channel data to a second channel in a DAW or music notation software, you can delete notes as desired from each of the two channels so that each one contain just the notes you want for the left-hand part and right-hand part.