05AB1E, 27 bytes (non-competing)
vyð¡RD¤…TheQsgα£Rðý})‚øí{ø¤ Explanation
vyð¡RD¤…TheQsgα£Rðý})‚øí{ø¤ Argument l v } For each y in l, do: yð¡ Split y on space RD Reverse and duplicate ¤…TheQ Last element equals "The" (true = 1, false = 0) sgα Absolute difference with length of array £ Get elements from index 0 to calculated difference R Reverse ðý Join on space )‚øí Pair each element with original {ø¤ Sort and get the original band name