We say that if a pair of different dog breeds mate, their offspring would be considered a but. However if these new designer dogs of two different breeds -their offspring are not a but but purée breed how is that?

They are not breeds they are still hybrids, When you consider that a designer dog usually costs more than either of it's purebred parents it simply seems that people have found a means to pad their pocketbook.
Here is some interesting articles.

'Designer dogs' or mutt, the costs are adding up - Business - US business - Bloomberg Businessweek - NBCNews.com (http://www.msnbc.msn.com/id/43715087/ns/business-us_business/t/designer-dogs-or-mutt-costs-are-adding/)

What's a Labradoodle—Designer Dog or Just Another Mutt? (http://news.nationalgeographic.com/news/2004/01/0115_040115_tvdesignerdogs.html)

You cannot take a labradoodle and a labradoodle (Designer mutts) and breed them to produce more labradoodles.

To create a breed, it takes MANY generations for a "labradoodle" to become an actual breed. The puppies that do not carry that gene should be culled and only the dogs that are of purest form of a "labradoodle" should be bred.

You would need many breed pairs so as not to line breed.

So.. the majority of people who create these papered mutts do not care what they breed to as long as they can create a cute "doodle" name to it.

I don't like designer breeds. I think its another fad for people to get tricked into paying big bucks for. Mixed dogs do not have a guaranteed personality. You have two (or more) characteristics and personality traits seeping through.

Designer breeds are not good. If any of the kennel clubs start accepting them into the breed shows, I will be highly disappointed.