The clause cited in the question does not contain the word "head," this is (properly) inferred in most major English translations from the surrounding context.
The word κατακαλύπτω, simply meaning to "cover" or "veil",1 can reasonably be broken into two roots: κατά + καλύπτω.
καλύπτω means "to cause to be covered in some physical way, cover someone (up)" or "to cause someth[ing] not to be known, hide, conceal, keep secret."2 Combined with the pronoun κατά, which in this usage indicates a "marker of extension or orientation in space or specific area..., of location that is relatively lower, down from someth[ing]."3, which in this instance is the object being covered, i.e. the head, this word clearly indicates that something is covered up or completely covered down from a specified object/location.
Even so, etymology is not the best indicator of the meaning of a word in a given context (although in this case it doesn't matter much).4 What is more important is how the word was used by contemporary writers in the context in which the word was written, and the word was used in extrabiblical literature during the same time period as Paul's writings to refer to young women's head coverings,5 and had also been used in the Septuagint in reference to covering (and uncovering) young women.6
Given the use of the word in Biblical and extrabiblical literature, the translation in the ESV is accurate.
1 William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), 517.
2 Ibid., 505.
3 Ibid., 511.
4 As an example, the word 'robot' comes from a Czech word meaning 'forced labor', referring to slavery. Clearly we don't mean that when we use the word today, which is why etymology is not always indicative nor even helpful for determining meaning in context.
5 Hermas, Visions, IV, ii, 1; Ps.-Dicaearchus, p. 144 ln. 16ff F. of the Theban women; and the word is also used in Josephus' Antiquities 7, 254 to refer to a king 'covering himself.'
6 The word refers to the facial covering of a prostitute (specifically, a woman pretending to be a prostitute) in Genesis 38:15 in the LXX. This word is also used in the Apocryphal work of Susanna, v. 32 in the Theodotion.