OLIVIA is an anagram of I (one) and VIOLA
Samuel Barber is a composer, and strap is a slang word for barber, after Hugh Strap in Smollett's "Roderick Random"
ran indicates an anagram but also in Shakespeare's Twelfth Night Viola, digsuised as a man, is a messenger between Olivia and Orsino i.e. she runs messages.