score:5
A bit unclear what you are asking. Presumably only English-language armies would use English words. But more generally,
Going into the Second World War, the [U.S.] Cavalry consisted of three Regular, four National Guard, and six Organized Reserve cavalry divisions as well as the independent 56th Cavalry Brigade. Because of a shortage of men, on 15 July 1942, the 2d Cavalry Division was inactivated to permit organization of the 9th Armored Division. White cavalrymen were assigned to the 9th Armored Division, and the all-black 4th Cavalry Brigade became a nondivisional formation.
In October 1928, a new era began as the [British] 11th Hussars became the first regular cavalry regiment to "mechanise", to change from a horsed cavalry role to a motorised one, re-equipping with armoured cars previously used by the Royal Tank Corps. Other regiments followed suit; in April 1939, the Royal Armoured Corps was formed to encompass the eighteen mechanised cavalry regiments of the line alongside the eight battalions of the Royal Tank Regiment
The [German] 1st Cavalry Division was formed in October 1939. It fought in the Netherlands, Belgium, France and on the Eastern Front. It was officially transformed into the 24th Panzer Division in late 1941.
Upvote:3
Another example: The 102nd Cavalry Regiment of the US Army was re-organised during WWII, to form the 102nd Cavalry Group (Mechanized). This fulfils the OP requirement of the men still being "cavalrymen."