Generic terms are not trademarks by definition.  That is, they can never receive exclusive usership rights under trademark law.   Generic "trademarks" are words or symbols that communicate what the product or service is categorically. 

For example, "shredded wheat" is a generic term that refers to the category of breakfast cereals that are composed of layers of crunchy wheat strips molded together into a pillow-type shape. This cereal may be manufactured by Kellogg's, Post or others, and each manufacturer is free to use the term "shredded wheat" to advertise their version of the cereal. This allows businesses to communicate freely with customers regarding what is product is actually being sold.  Giving one company a monopoly over "shredded wheat" would mean nobody could compete fairly to sell that cereal. Thus, generic words are never trademarks because that would grant a company a monopoly in the product itself, not in a word or symbol.

Two-Part Test of Genericness

The US Patent and Trademark Office says this about generic terms:

There is a two-part test used to determine whether a designation is generic: (1) What is the genus of goods or services at issue? and (2) Does the relevant public understand the designation primarily to refer to that genus of goods or services? H. Marvin Ginn Corp. v. Int'l Ass’n of Fire Chiefs, Inc., 782 F.2d 987, 990, 228 USPQ 528, 530 (Fed. Cir. 1986). The test turns upon the primary significance that the term would have to the relevant public.

The Trademark Office examining attorney has the burden of proving that a term is generic by clear evidence.

Treatment of Compound Words

Combining a generic word with another generic words may or may not overcome the generic treatment of the newly formed compound word. This depends on whether the new word itself is the commonly used term for the object being sold.