Count: 0 — There are no attested Roman given names or family names that begin with the letter K in classical Latin sources. This matters for writers, parents, genealogists, students of classics, and curious readers who seek authentic Roman praenomina, nomina, or cognomina. Interesting detail: the letter K existed in the earliest Latin alphabet, but classical Latin almost always used C for the /k/ sound, so K rarely appears in surviving Roman name lists.
Classical orthography and Roman naming practice explain this absence. Standard reference collections and corpora of inscriptions and literature (for example, the Corpus Inscriptionum Latinarum, the Prosopographia Imperii Romani, and major Latin dictionaries and repertories) record praenomina, nomina, and cognomina beginning with C, G, Q and other letters, but not with K as a regular initial. K turns up only in a few archaic spellings or in foreign and late-period borrowings; it also appears as an abbreviation in inscriptions (for Kalendae). For a strict, well-attested list of Roman names, the search term “Roman names that start with K” therefore yields no reliable results.
If you want a Roman-style name that looks or sounds like it begins with K, use authentic Latin names starting with C that represent the /k/ sound (for example Caius, Claudius, Cornelius), or choose Greek and later names that are sometimes written with K in modern transliteration (e.g., Kleopatra as Cleopatra in Latin). Allow rare archaic variants such as Kaeso (an old spelling of Caeso) only with the caveat that they are exceptional and sparsely attested. Consult primary epigraphic corpora, the Oxford Classical Dictionary, and reputable onomastic databases when you compile verified Roman names.