Star Dog.com (スタードッグ.コム) is an alternate version of Dog.com, with a different set of personalities, which is not confirmed to have been released. It was supposed to be released in June 2001 for 14,800 yen, according to a Game Watch news article, and the toy's box and a card with info about it was displayed at the 2001 Tokyo Toy Fair. You can see the card and box only partially in the above photo with Monkey.com, which also does not appear to have been released.
"Star" in this context refers to a popular person.
Star Dog's personalities include:
Star Dog.com apparently may have a color scheme that's different from the ones Dog.com has??