You can change the color of digital illustrations very easily within an array of graphics software. I'll list the most common solutions below.
Please note: The following steps are to change the color of transparent PNG images. If you're trying to change the color of a Vector file, the process should be as simple as selecting the illustration and changing the foreground color within your software.
Photoshop ($$$): Right click on the layer that contains the illustration > Select 'Blending Options' > 'Color Overlay' > Select your color.
Affinity Designer ($): Select the layer that contains the illustration > Click the 'FX button (within layer panel) > 'Color Overlay'
GIMP (Free): Set the alpha lock for the layer (checkerboard icon in the "Lock" line at the top of the layers list) > Bucket-fill the layer (without any selection) with the required color, the alpha lock will ensure the opacity of pixels isn't changed.