The ornamental design for a paintbrush handle, as shown and described.
FIG. 1 is a front view showing my new design with the rear view being a mirror image thereof;
FIG. 2 is a side view with the opposite side view being a mirror image thereof;
FIG. 3 is a top view thereof; and,
FIG. 4 is a bottom view thereof.
The broken lines and stippling shown on the drawings for the bristles and bristle holder is for illustrative purposes only and forms no part of the claimed design.