Who lends his name to an expression that describes the random movement of particles in fluids?

Robert Brown for whom we get the term Brownian motion which he first described in 1827. Brown was a Scottish botanist who classified several plant species. He also was the first to describe the cell nucleus of plant cells.

Brown was investigating the fertilization process in Clarkia pulchella, then a newly discovered species of flowering plant, when he noticed a “rapid oscillatory motion” of the microscopic particles within the pollen grains suspended in water under the microscope. Other researchers had noticed this phenomenon earlier, but Brown was the first to study it.

Most science folks are more familiar with Einstien's work on the Brownian motion of atoms and their wobble based on the surrounding conditions. Einstein actually won his Nobel prize for his research on Brownian motion...not his much better-known Theory of Relativity...

https://www.britannica.com/science/Brownian-motion