Note, this does not allow dynamic updating of the picture (every time you update the game variable's value, you will need to do the picture script call)
$game_screen.pictures[NUMBER].show($game_variables[1], ORIGIN, X, Y, ZOOM_X, ZOOM_Y, OPACITY, BLEND_TYPE)
replacing the constants above with actual values...
NUMBER = which picture ID to show (generally 1~100)
ORIGIN = upper-left (0) or center (1)
X/Y = screen coordinates
ZOOM_X/_Y = percentage to zoom in/out picture, default is 100
OPACITY = transparency, default 255
BLEND_TYPE = normal (0), add (1), sub (2)
...and the game variable ID accordingly.
Alternatively, you can change Game_Picture's name attribute to accessor:
attr_reader :name # file name
into
attr_accessor :name # file name
And use the script call:
$game_screen.pictures[NUMBER].name = $game_variables[1]
Assuming all you want to do is change the graphic it uses and nothing else.