The list of Categories can be found in Lookups, Category. This is where to create, edit/rename, or delete Categories.
Category Name is an attribute of Asset Type. When editing an Asset Type, an existing Category can be selected. Any Asset of a particular Asset Type will have the Asset Type's Category.
When viewing a fixed asset or the asset list, Category Name is viewable, but not editable.
If you are creating a new Fixed Asset, when you choose the Asset Type, the Category Name is automatically populated from the Asset Type.
If you are creating a new Multi-Quantity asset, you can choose an existing Category Name, because a MQ asset acts as its own Asset Type.
When editing an existing Multi-Quantity asset, if you press the down arrow key while the field is populated, you only get the current Category. To choose from the full list of existing Categories, first clear out the field, then press the down arrow key.