What is the name of a half wall with posts on top that divides a space into two?

A non jargon terminology (i.e. non scientific architectural) would be permanent room divider or wall divider or plain divider.

Probably the proper architectural terminology is mullion is a vertical element that forms a division between units of a window or screen, or is used decoratively

Figure: Mullion (image source: Wikipedia)

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In French you mint find it as paravent, which comes from the latin paravento (which translates for the wind).

The use of permanent is to separate what you are looking for from room dividers like

Figure: room divider source:vkf-renzel.com

Some architectural terms:

• Cancellus (plural: Cancelli) Barriers which correspond to the modern balustrade or railing, especially the screen dividing the body of a church from the part occupied by the ministers hence chancel. The Romans employed cancelli to partition off portions of the courts of law.

• Muntin A vertical or horizontal piece that divides a pane of glass into two or more panes or lites in a window.

• railing (also related handrail and banister)

Figure: Railing (source : www.houzz.in)

• (JimClark also suggested) Partition is another word that can refer to the vertical wall in a room. (This is something that I also thought of, but -initially- I decided not to include because in my mind partition refers to the horizontal spaces that are created by the vertical column).