Yes, you can make a label style for the geometry points that labels to either side you want. Make a new style from your current style and modify things like rotation, anchor points, and justification to get the same look, just reversed.
Now you can apply that new style to the goe point labels for one of your alignments. You can even apply different label styles to be used in certain station ranges along the same alignment. (similar to the way a corridor uses assemblies)
If you just need a few labels flipped you can skip the above suggestions and select the label, right click, and choose 'flip label'.