Understand you are talking two things here. A trademark is a name you use in commerce. You get rights to it by using it in a way that is distinctive, non-descriptive, and not in conflict with others. Registration is something you can do to marks you are using (or will state intent to use) that will give you some additional options when it comes to enforcing your mark.
Company names can be, but are not necessarily, trademarks. A famous example is the Subway (which is a registered trademark) sandwich chain which is owned by Doctor's Associates (not a trademark).
Trademarks are typically adjectives. It's a SUBWAY restauraant. You can use any number of these to describe your products if you want protection Creating trademarks just takes some creativity of your part and using it in commerce. You can declare that you intend this as your brand by using the ™ symbol or explicitly saying X is my Trademark. Then you can decide if you want to go to the expense of registering the name.
You don't need a trademark on each product if you don't want. Many product names are descriptive. While "Kraft" has a trademark on "Plantars" they don't trademark (and are not eligible to) trademark Peanuts, Cashews, Mixed Nuts, etc...