Some examples are below (source: https://www.etsy.com/shop/JazzberryBlue). How do I achieve gradients like this in Gimp? Or if not Gimp, what is the general process for creating gradients that blend with this kind of "spray paint"/ink texture? Is there a name for it?
IMHO a combination of a banded gradient with soft edges/transitions:
This gives this:
With a little bit of Spread noise added:
The image you show is probably such a gradient applied to a grayscale image using
Colors > Map > Gradient map.
I don't think this is a gradient, at least not one that was created using the gradient tool. It's too irregular.
I would begin with something like this. These were just painted with a soft edged brush. You could make them more irregular than I did.
Then use the Warp Transform Tool, using the Grow Area setting to create something like this. To do this I set a large brush size (larger than the circle shown above), with about 95% hardness and quite a low strength setting. I then warped the image until it created a narrow black edge, then I reduced the brush size and hardness, and made some softer warping in the middle.
Then I used the HSV noise filter to add a texture
Here's another example, just messing around with more irregularities, and the different Warp tools.