Keep asking until we get the answer we want -- What is the term for
the form in which a brand name represents the class of items?  Could
it be g --- ...

(Is the term "form" correct in this context? -- don't answer that.)

When a brand name comes into general usage to represent a class of
items, the name is said to have been "genericized" or to have
undergone "genericization." "Generified" and "generification" are used
in a similar sense.

At the end of this article, you'll find a long list of trademarked
names that are often used generically, including "Jacuzzi":

"Genericized trademarks (or, in British English, genericised
trademarks) are former brand names, once legally protected as
trademarks, which have since come to signify a generic product
regardless of its manufacturer."

Wikipedia: Genericized trademark
http://en.wikipedia.org/wiki/Genericized_trademark

"Jonah Goldberg posts to The Corner that 'Blogger' might go the way of
'Xerox,' 'escalator,' and, probably soon, 'Kleenex' and 'Band-Aid.'
That is, its brand name is being used to describe the whole process of
web logging, meaning Blogger may soon lose the rights to 'blogger.'

It's one of the pitfalls of breaking new ground in business -- you
then have to spend millions to ensure your name doesn't become
'generified.' Trademark law says you have to actively defend your
brand, else it be co-opted by competitors."

The Agitator: Contramundum
http://www.theagitator.com/archives/000912.php

A more academic name for a brand name that becomes a common term for
its class is "proprietary eponym":

"An eponym is a general term used to describe from what or whom
something derived its name. Therefore, a proprietary eponym could be
considered a brand name (product or service mark) which has fallen
into general use.

We've all seen it happen. The trademarks of today become the household
word of tomorrow."

Database of American Proprietary Eponyms
http://www.prairienet.org/~rkrause/brands.html

Google search strategy:

Google Web Search: genericized OR genericization name
://www.google.com/search?hl=en&ie=UTF-8&q=genericized+OR+genericization+name

Google Web Search: generified OR generification name
://www.google.com/search?hl=en&ie=UTF-8&q=generified+OR+generification+name

Google Web Search: "proprietary eponym"
://www.google.com/search?hl=en&ie=UTF-8&q=%22proprietary+eponym%22

I hope this helps! If anything is unclear, please request
clarification, and I'll get back to you as soon as I can.

Best regards,
pinkfreud

Excellent.  I like "proprietary eponym."  And I'm glad to know there's a database.

Somehow, this segues to a story about someone describing a dream,
seeing a battle between clothing and footwear...

... and someone shouting, "T-shirt! Leave those Keds alone!"

Many thanks for the five stars and the nice tip!

And a special thank-you for the Pink Floyd wordplay. It's music to my
ears, even though normally I don't need no waltz around me. ;-D

~Pink