When transcribing the names of contemporary people, you should follow the usual rules of English-Russian transcription. Thus said:
Note that transcriptions above reflect rules codified by Gilyarevsky and Starostin, Kuznetsova and others.
They do not necessarily reflect the actual pronunciations of the names by American or British English speakers (or in fact any variety of English) and are results of multiple compromises made when developing those rules.
Those rules are not in any way comprehensive, nor widely known to general public. That's why, especially with the advent of the Internet, you might find name of the same person transcribed dozens of ways. You can find Samuel Jackson's name transcribed as Самуэль, Самуэл, Самюэль, Сэмюэл, etc., with pretty much every possible combination of open/close versions of all three vowels and palatalized/unpalatalized final л.
When transcribing the names of historical persons, or European monarchs, or Christian saints, or in multiple other special cases, you should use historically accepted transcriptions of those names (or their origins):
Samuel the Prophet Пророк Самуил
Queen Aahmes Царица Яхмес
Jeffrey of Monmouth Гальфред Монмутский
Edward Longshanks Эдвард Длинноногий
Lawrence of Arabia Лоуренс Аравийский
Neil of the Nine Hostages Ниалл Девять Заложников
Simon Peter Симон Пётр