Originally it was called «The Teenagers», later «The Wailing Rudeboys», one more later «The Wailing Wailers», and finally «The Wailers»

Thus, the word "wailers" means people who cry or complain in a loud voice because of pain or grief.
As for its Russian equivalents, they are:
-рыдающие
-стенающие
-завывающие
-вопящие
-причитающие
-плачущие
As far as I know, in Afro-American tradition, wailing is rather popular.

wail - thesaurus entry

VERB
Related thesaurus entries
wail/howl/scream like a banshee

1 to shout or cry with a long high sound to show that you are in pain or are very sad
*Synonyms or related words for this sense of wail*
To cry, or to start crying: cry, burst out, dissolve into, weep, choke up, sob, wail, howl, snuff...

2 to make a long high sound
*Synonyms or related words for this sense of wail*
To make a high sound: beep, bleep, chime, chink, click, clink, creak, keen, mewl, peep...

взято с http://www.macmillandictionary.com/

я считаю, что Боб Марли назвал свою группу "The Wailers", что переводится как "Плакальщики" потому, что искренне сочувствовал своим собратьям. Также, по моему мнению, он этим названием хотел передать свои мысли и желания, например, призывал творить добро, любить окружающих, и никогда не воевать!

To my mind, Bob Marley called their band "The Wailers" because their songs are like prayers, as though they cry. They also sing songs which incite to action (such as "The War"), their songs can help people in difficult times (for ex."No Woman,Dont cry")

In 1963, Bob Marley, Bunny Wailer, Peter Tosh, Junior Braithwaite, Beverley Kelso, and Cherry Smith formed a ska and rocksteady group, calling themselves "The Teenagers". They later changed their name to "The Wailing Rudeboys", then to "The Wailing Wailers", at which point they were discovered by record producer Coxsone Dodd, and finally to "The Wailers". By 1966, Braithwaite, Kelso, and Smith had left The Wailers, leaving the core trio of Bob Marley, Bunny Wailer, and Peter Tosh.

Bob Marley & The Wailers were a Jamaican reggae, ska and rocksteady band formed by Bob Marley, Peter Tosh and Bunny Wailer in 1963. Additional members were Junior Braithwaite, Beverley Kelso, Cherry Smith and Aston and Carlton Barrett. The band came to an end with the death of Bob Marley in 1981.