The House of Hanover was renamed the House of Windsor during the reign of Queen Elizabeth II's grandfather George V when World War I made it quite unfashionable to have a German monarch. Thus, George V was both the last Hanover monarch and the first Windsor monarch.
Oh yes, for you purists, I do realize there were three place-holding Stuart monarchs after James II, the last Stuart descendent alive when the Stuarts were first booted out, was given his walking papers in 1688. His father, of course, was the notorious Charles I, who forfeited his head as well as his throne in 1649.
The House of Hanover became the House of Saxe - Coburg after Victoria married Albert. This became the house of Windsor at the time of Geo V.
Frankly the only house they should be in is the jailhouse.