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They do have their own names!

The Periodic Table is actually split up into far more groups then just the metals and non-metals.

The groups actually are as following:

The Alkali metals

The Alkaline earth metals

The Lanthanides

The Actinides

The transition metals

Other metals

(all of the above are collectively grouped as the metals.)

The Metaloids (these can neither be definitely grouped as metals or non-metals as they share properties of both.)

Other non-metals

The Halogens

The Noble gases

(these are collectively grouped as non-metals.)

The reason for the fact that the collective groups being known as just the metals and non-metals is most likely due to the fact that there are far more metals, so it is more likely that these were discovered and then named first.

There is no strong definition on what is a metal or non-metal, however, non-metals can generally be defined by having a negative valence whereas metals have a positive valence.

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