First the product.
Cool idea...I would not buy it, but maybe as a gift, but it would need to be at a lower price point. Maybe in the $25 to $40 range depending on size. I like that it folds into a pillow. One other idea I thought of is possibly the ability to zip or button the pockets up or down. Same with the compartments. Then you have the duel usage as a regular blanket. Also it may be worth selling by the typical sizes - throw, single, full, queen, and king.
I agree that the name needs some work.
Website
In general but the shopping page especially takes a long time to load. Maybe consider showing one picture and then a sample square of the other colors. I am not sure if this would help, but showing one picture but being able to click on it and have a "slide show" of the different options, and close up of the features.
I think this would help on the purchase page too. Have one page that has a pull down for the color and one for size.
The 3 paragraphs under watching in style are very wordy and not quick and easy to understand. Consider making them short bullet points.
Looking ahead at the up coming holidays. Valentine's Day - A way to cozy up to your significant other, Mother's and Father's Day.
I would combine the customer service and return page. Also I think people would be more familiar with putting FAQ. Consider adding to the FAQ washing instructions.
In general try to write everything as concisely as possible. Less paragraphs and more bullet points.