The phrase using [or choosing] the generic term may be the clearest way of saying it.
Trademarks are brand names for goods or services that are owned and controlled by the owners of those terms. Contrary to some of the comments, the use of trademarks without the owners permission may be a violation of rights, even when the unauthorized user is not a direct competitor doing it for moneymaking purposes. Publishers and dictionaries are often challenged when they use a brand name for goods not from that brand's owner.
Genericized trademarks are terms that used to be owned by one source, but that owner has lost ownership, most often because they did not exercise control over that mark, either in their own use or in the use by others. Classic examples of that are escalator (formerly owned by Otis), aspirin (formerly owned by Bayer), and zipper (formerly owned by Goodrich).
There are many brands that are often used in common speech in a generic way. If the owner is careful to prevent commercial usage, they may preserve their ownership and control. Kleenex, Band-aid and Xerox are all terms that are often informally used to refer to their generic equivalents, but there owners continue to protect them, and they cannot be used in commercial materials as the descriptor of the generic.
True generic terms are the basic descriptors of goods or services that were never trademarks. Facial tissue, bandage and photocopying are all basic generic terms.
The hard-core trademark purists even go so far as to suggest that, when using trademarks, you should combine the trademark with the generic term, as in LEGO® toy building blocks, or Kleenex® facial tissues.
Unfortunately, you cannot use the term genericize to refer to the use or selection of a generic term since that means to convert a trademark into a generic term.