1 Corinthians chapter 13 need not have been known as an independent text for it to be considered a hymn. The question does not ask whether Paul actually wrote this material or simply inserted what was already a much-loved hymn, or whether the hymn was added later, as some critics suggest. It is considered a hymn because of its literary qualities. The Little Rock Catholic Study Bible says that all or part of the material may once have been an independent piece in the style of Hellenistic eulogies of virtues, but it is now integrated, by editing, into the context of 1 Corinthians 12-14 and into the letter as a whole.
A hundred years ago, A.Harnack wrote of The Apostle Paul's Hymn of Love. In Part VI (page 489ff) he describes the literary quality of the hymn, which he says ranks highest amongst all the writings of Paul in respect of its form. It offers the most sublime and strongest aesthetic charms, without being poetry in the strict sense. In Harnack's description, rhythm and poetic form flowed from enthusiasm - an obvious proof that the deepest contemplation and sensibility became, by inner necessity, poetic in their expression. Lastly, it is the subject matter which in its powerful expression gives the effect of perfect poetry.
The hymn is divided into three parts, and a final verse : the indispensableness of love (vers. 1-3), the nature and effect of love (vers. 4-7), the eternalness of love (vers. 8-12). Each part has its particular scheme; but in all the parts the highest effects are obtained by the excellent choice of words, by the powerful simplicity of the syntax and the combined means of antithesis and repetition. Harnack devotes more than three pages to a description of the literary quality of this hymn.
Anthony Thiselton commented in The First Epistle to the Corinthians, “Chapter 13 has an exalted style that stands out from its literary context, and should be seen as a brief encomium, which in ancient rhetoric was a speech in praise of a hero or, in this case, a virtue.”
Wikipedia tells us that The word hymn derives from Greek ὕμνος (hymnos), which means "a song of praise". It can be addressed to a deity, but need not be: in this case it is in praise of love. More than anything, the exalted style marks this "hymn of love" as a true hymn.