Apple, the world’s most valuable technology company, is seeking a trademark for “iWatch” in Japan as rival Samsung readies its own wearable computing device. The iPhone maker is seeking protection for the name, which is listed in a category for products such as a handheld computer or watch, according to a June 3 filing with the Japan Patent Office that was made public last week. Takashi Takebayashi, a Tokyo-based spokesman for Apple, didn’t respond to a request for comment. Apple’s shares have retreated more than 40 percent from a record high in September amid concern that Chief Executive Officer Tim Cook has taken too long to deliver a new breakthrough product to help make up for stiffer iPhone competition. The company has a team of about 100 product designers working on a wristwatch-like device that may perform some of the tasks now handled by the iPhone and iPad.