Carefully pry open the case from the bottom edge.

Boy, this is a lot easier to open than an iPod! (Spudger not required.)

On the inside of the back cover, you'll find the product label. Notice the official company name, Tokyo Tsushin Kyogo Ltd. I've seen photos of later versions of the TR-63 which say "Sony Corporation" there instead.

I'm not sure what happened to the corner of the label - perhaps after all these years in the back of my closet it was likely eaten by a grue?