What does Rayyan mean?
From the triliteral root r-w-y (ر-و-ي, 'to be quenched with water, irrigated'), meaning 'luxuriant, well-watered, lush'. Ar-Rayyan is also the name of one of the gates of Paradise through which those who fasted are said to enter, which drives much of the name's popularity.
What does Sami mean?
From the root s-m-w (س-م-و, 'to be high, elevated'), meaning 'elevated, lofty, sublime, eminent'. Note the distinct name Sami' (سميع, 'all-hearing'), which comes from a different root (s-m-'); the two are easily confused in transliteration.