Different royal houses ruled different nations.
The Renaissance period, in England, began in the 1400s and ended in the 1600s. During these two centuries, many royal houses ruled.
The House of Lancaster
Henry the IV, V, and VI ruled England between 1399 and 1461.
The House of York
Edward IV ruled England between 1461 and 1470.
The House of Lancaster (2nd rule)
In 1470 and 1471, Henry IV took over reign again (last in control in 1461.
The House of York (2nd rule)
In 1471, the House of York took the reign back from The House of Lancaster. Edward IV, V, and Richard III ruled England from 1471 to 1485.
The House of Tudor
The House of Tudor took over power in 1485 with Henry VII. Their reign extended from 1485 through 1553 (following Henry VII with Henry VIII and Edward VI.
After Edward VI reign, things became complicated. Edward Vi named Lady Jane Grey as the new heir (she was only ruler for 10 days in July of 1553). Following her was her husband, Philip who ruled from 1554 to 1558. Later, Elizabeth I ruled (1558 through 1603).
The House of Stuart
The last royal house to head England during the Renaissance was The House of Stuart (under James I and Charles I--1603-1649).