The core  of amides is called the amide group (specifically, carboxamide group).
In the usual nomenclature, one adds the term "amide" to the stem of the parent acids name. For instance, the amide derived from acetic acid is named acetamide (CHCONH). IUPAC recommends ethanamide, but this and related formal names are rarely encountered. When the amide is derived from a primary or secondary amine, the substituents on nitrogen are indicated first in the name. Thus, the amide formed from dimethylamine and acetic acid is N,N'-dimethylacetamide (CHCONMe, where Me = CH). Usually even this name is simplified to dimethylacetamide. Cyclic amides are called lactams; they are necessarily secondary or tertiary amides.