Max Bell from Number One noted that the song finds D'Arby "in his quiet, sensitive, loving disguise, as opposed to his crafty, naughty, whoopsadaisy ma'am alter ego." He also felt that "Sign Your Name" "testifies at least to a knowledge of soul", and concluded, "From a Heaven 17 influenced beginning a fair single starts to brood but this could be a sucker punch rather than a knockout."[3] Roger Morton from Record Mirror commented, "'Bop shoo wop wop/Bop shoo wap wap'. Terence has joined Showaddywaddy? Sadly not. This is the fourth single from the Hardline album, a crooner not a rasper, with some fine quavering from Tel's tonsils and a rhythm closely related to that of Scritti Politti's 'The Sweetest Girl'."[6] Another editor, James Hamilton, wrote in his dance column, "Moodily shuffling sad 109/54+1⁄2-0bpm lament, not really for floors".[7]
Sheryl Crow released her rendition of the song in 2010 as the second single from her eighth studio album, 100 Miles from Memphis. It features Justin Timberlake on background vocals.[30] The music video, directed by Wayne Isham, was released on September 16, 2010 through Crow's VEVO account.[31]