Add a Hue/Saturation adjustment layer above your "Button" layer.
You can add the layer either from the toolbar: Layer → New Adjustment Layer → Hue/Saturation…
Or clicking the adjustment layer button from the bottom of the Layers window and then choosing Hue/Saturation…. The button is a diagonally split black & white circle:

The changes in the adjustment layer will affect the gradient effect on the "Button" layer.
Your outcome could be, for example:

A whole different approach would be to adjust the gradient effect so that it fades from (partially transparent) black to 100 % transparent and maybe, in addition, tweak its Blending mode:

The upper knobs adjust the gradient stop's opacity and the lower knobs the stop's color.
As Alan mentioned you should now change the shape's Fill back to 100 %. Also you might notice that plain 0 % black to 100 % black gradient might look too harsh, so you could either
- Tweak the color stops' opacities or …
- Tweak the whole gradient's opacity to get the desired effect.
As you probably are trying to mimic shadow/lighting effects, it might be a good idea to change the gradient's blending mode to either any of the shadowing blends (from Darken to Darker color in the list) or one of the blends specifically designed for lighting (Overlay to Hard mix). Here I'm using the gradient with 30 % opacity and Multiply blend:

Then one could change the color of the whole layer by just changing its fill. Problem is, in your case, the other effects as well: a red color is defined also in Inner shadow and Stroke.
Consider changing the Inner shadow's color to white, reduce its opacity and change the blending mode to one of the either bleaching (Lighten—Lighter color) or, again, lighting blends. Say, white inner shadow with 40 % opacity and blended with color dodge could do wonders in your case.
Stroke, on the other hand, doesn't affect the colors of the layer it is applied to but it's background i.e. the layers beneath it—even when its position is set to Inline. You will not get the desired results if you change the stroke's gradient to black 0–100 % opacity gradient. However, you could consider adding an Inner glow effect with 1 px size and 100 % choke; then play around with its colors/gradients as above.
This would, though, work only with layers that have a fill—such as shapes, which your "Button" layer is.