Hold the phone and photo album!
Please don`t turn people off by saying so much stuff up front about you. (i.e. just your name is more than enough and often you don`t even need that if you have a name tag on)
Have you been to networking group and really watched how people react to you? I have done lots of people watching. And in most situations, what I find is that you have 7 to 10 words before their eyes start looking elsewhere, even if you`re standing in front of them. It`s so much better to not use that time up with things they won`t remember anyway ;)
So I might start
Hi my name is __ Do you know someone who has a special dog? or maybe Do you know someone whose dog is part of the family? (wait for answer) Well what my company does is (benefits of your products) we provide (exactly what products) and we`re embroider their names or initials or your family name on the clothing if you`d like that, too.
Like --and this is a first draft from a cat lover ;)
Do you know someone whose dog is part of their family? Well, what I do is help help dog lovers all over the world to pamper their favorite pet by providing durable, sturdy _____. And we can make the clothing extra special by embroidering the dogs name, initial or your family name on the clothing, too. (then I`d have another quesiton at the end, so that they can verbally connect with you again)
Cause really, if you bottom line it, your name, title, etc. don`t mean anything to a stranger. A stranger wants to know first and foremost "whats in it for me" i.e. how is knowing you going to help make my life better in some terrific way.
At networking events, what you`re looking use your introduction to get them to give you their cards, so you can follow up. So consider asking those who already purchased from you, why they purchased - what did they find in your products that made them feel better about their lives.
I would think words like "cute" "compassion" as well as warm, cool, stylish, fun, special, pick their own colors, might be some words they could use, although I`m a cat lover myself.
PS. Based on the colors of your website, I`d think that your idea client is a women. And that might be something to consider when writing your elevator speech. Green is also a color to be careful with as 20% (of men, if I remember the number correctly) are color blind and don`t see green.