Yes it's criticality important from a SEO point of view.
Researching the basics of image SEO. We found, when we were doing correlation analysis, that images and specifically the alt text that's inside of them are a remarkably well-correlated metric for SEO. Besides just being useful for people, images are also, it turns out, useful for search engines. I think part of the reason behind that is that pages that are well developed tend to also have images on them because it helps portray information in a way that textual based content can't do.
Let me go over some of the important factors with image SEO. Number one, I already mentioned this a little bit, is alt text. Alt text is the text that you provide for an image in case it can't be displayed. Maybe the image is gone or maybe someone is using a program that can't display images. This is the text that takes it place. So it makes a lot of sense from an SEO perspective that this metric is going to be important because it's the information you tell the search engines and other technologies what the image represents. With these, I recommend keeping them below about 140 characters. It's a rough rule of thumb. Also, have them be descriptive and in line with what you're trying to target for that page.
Number two is the file name. This works off the exact same principles. The file name is also information you give directly to the search engines and to other technologies to identify what the information is about. I would gander, if you will, that the file name is probably a rougher signal than the alt text. Alt text, from my experience, when it's there, which is not all the time, in fact, alt text is not included many times which is bad for SEO. But when it is included, it tends to be a clearer signal than a file name which a lot of times is just algorithmically generated by the timestamp, so it's just a bunch of numbers.