Ben Jonson (with no "h") wrote at least two poems called "Song to Celia" (or "To Celia" for short), so there must have been something about that name that he really liked. (Shmoop thinks Celia is a nice name, too). It has been said that the name comes from the Roman family name Caelius, which in turn is thought to originate from the Latin caelum ("heaven"). That sure seems an appropriate name for someone the speaker claims he loves.
Beyond its telling origins, however, the name Celia also has a long literary history. It is a fairly common name in ancient pastoral poetry and romance, and Jonson was a big fan of classical (ancient Greek and Roman) literature. In addition to its ancient literary pedigree, Celia is also the name of one of the characters in Shakespeare's pastoral comedy As You Like It (1599 or 1600). Jonson knew Shakespeare, and it's totally possible that Big Willy's use of the name had at least something to do with Jonson's choice. In the decades following Jonson's death, Celia would become a frequently-used name in English pastoral poetry, appearing most famously (or notoriously) in Jonathan Swift's bawdy poem "The Lady's Dressing Room." Want to read Swift's dirty little poem? Check it out here.