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.
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.