Does Google care about the image filename

The answer is Yes. Images are always hard to index so try to use a logical name.

Eg. an image about Tools:

The location is: http://www.joomlasearchengineoptimization.nl/images/stories/Tools.jpg

Google can understand that this picture is in the category stories and that its about tools.

If you would use this name:

http://www.joomlasearchengineoptimization.nl/images/stories/T.jpg

Than the "T" doesn't tell anything about the image wich makes it difficult for Google to estimate what it's about

For more information a video by Matt Cutt: