Does this fingery style have a name?

Edit: Photoshop probably provides better edibility, but naturally the pixel output has drawbacks.

Sponge Fingers

I had those designs on a plate when I was 7...

To me it looks like another definite evidence that shows that the Apollo 11 mission was a hoax. They were not there.

I'd call the style "not11".

Trying dragging the image into Google Search and see if it finds anything.

I do not think every style has a name......

Spoon Graphics had a few tutorials about this style of production. This was one of them.How To Create a Flat Style Vector Planet in Illustrator

It looks like it could fit in with the interior decor of the Death Star.

I used the Search with an image feature on Adobe Stock to see if there were any similar images and find out what they were called. I found one called Abstract background with colorful melting shapes (#175641020). I tried a Google search with the keywords "abstract melting shapes vectors" and found some more, so that might be what they're called.

I think it should be called 'blobulation'. Then you could say things like 'As you can see, I have blobulated this image', or 'I have introduced blobulation to this design for a more contemporary feel'.

I would call it "Modern simplified Japanese woodcut clouds"