Aha! Now I understand, and this should actually be fairly simple. You don't even need to merge the shades in your image (though you can choose to do so, if you wish), you just need to adjust the selection parameters of your tool.
Both the Fuzzy Select and Color Select tools allow you to adjust the sensitivity of their color matching via two parameters, "Threshold" and "Select by:". Threshold sets the "width" of the range for what it considers a match to the pixel you click on, and Select-by allows you to control what color parameters that range applies to.
Normally, Select-by is set to Composite (meaning, it considers all aspects of the pixels' color) and the Threshold is set to 15. If you simply want your selection to encompass all of the various shades of pink in your logo, widening the Threshold might be enough to accomplish that all by itself. If that doesn't help, or if it begins to pull in colors you don't want, you may get better results with a different Select-by mode.
Select-by can be a little non-intuitive, since it operates very literally on the pixels' color values. It can help to use the eyedropper tool's "info window" (which you can bring up by shift-clicking on a pixel with the tool) to get an idea for what sort of color values you're dealing with. Several values of pink may all have similar Red components, or they may have very different red components, but all have very similar Green or Blue components — you'd want to Select-by the one on which they're most similar, and set your Threshold accordingly. Often, the Hue parameter can be a useful one for selecting different shades of a similar color, but unfortunately the Hue value for red/pink is 0°, the same as it is for white/black/gray. So in this specific instance, Hue probably won't be of much use to you unfortunately.
Using the fuzzy/color select tool while holding down the Shift key, to add to the current selection, can also be a quick way to combine the selection of multiple ranges. So, rather than over-extending the Threshold (and accidentally sucking in shades of gray, or some other color), it may be more helpful to simply fuzzy-select the primary color in the logo, and then shift-select to add the highlights/lowlights into the selection. You can also Control-click to subtract from the selection, to remove any areas of background color that might get pulled in.
Once you've built up a selection area containing just your logo, you can use the Bucket Fill tool to make your entire selection the same color. (You could theoretically do the same work in one step, since the bucket fill tool supports the same Threshold and Select-by parameters, but since that can be kind of unpredictable it's usually better to build a selection area first, then use the bucket tool to "Fill whole selection".)