The general name for a pure substance containing different atoms chemically joined together is a compound.

Here's why:

* Pure substance: Means it's made up of only one type of material.

* Different atoms: Indicates that the substance is composed of at least two different elements.

* Chemically joined: This signifies that the atoms are bonded together through chemical bonds, forming a new substance with properties distinct from its constituent elements.

Examples of compounds include:

* Water (H₂O) - Hydrogen and Oxygen

* Salt (NaCl) - Sodium and Chlorine

* Sugar (C₁₂H₂₂O₁₁) - Carbon, Hydrogen, and Oxygen