What are these white connectors called?
Those are "wire-to-board" connector assemblies. You need to look for hints on its brand as the one you have there is a matched mated system. An important specification to aid identification is the pitch or distance between the center-lines of two pins: usually either 0.1in (2.54mm) or 0.156in (3.96mm).

Although the picture is a bit unclear, I think what you have there is a TE 0.1in connector from their CST-100 system. Try this page and check if the product photo and the 3D PDF matches your connector.

When faced with an unknown connector, try exploring catalogs like the one from RS or TE's picture search.