Well, then, name the Teddy Bear ??
Teddy = Edward, Eddie, Theodore but Edward would be most appropriate when Vivian (whatever you want me to be!!) aka Julia Roberts aka Pretty Woman aka the most expensive WL ever (not the $3,000 for the week! but she did score the billionaire at the end) climbed into Richard Gere's Lambrogini and took him for the ride!! Edward is the name and as Vivian called him Eddie the morning after, so will I.
Therefore, my suggestion will be:
Eddie, The Teddy Bear
May all punters be Eddie and all WLs be Vivian, she wanted a Fairy Tale, why not ??
And it is only fittingly that you name your teddy after the best ever punter, who is a billionaire, drives a sporty car, pick up a WL from the street of LA, took her back to his suite at the Beverly Wilshire Hotel, paid for the hour ended up extending that to overnight and the morning after offered $3,000 for the week and eventually .................. well, we all knew the happy ending do we??
Cheers