Count: 0 — Note that no female given names of clear Irish or Gaelic origin begin with the letter Z that meet the stated criteria. Require only authentic Irish/Gaelic names or historically attested forms, and Z does not appear as an initial letter in native Irish name lists. Add an interesting detail: Irish orthography and traditional name records rarely use the letter Z, so Z-initial names in Ireland are almost always later borrowings or anglicised imports rather than original Gaelic names.

Accept that the absence has clear historical and technical reasons. Use authoritative references such as Ó Corráin, Foras na Gaeilge, and Irish birth and name registries, which show no native Irish female names that start with Z. Follow the historical Gaelic alphabet and spelling patterns: Z is not part of traditional Irish orthography and appears only in loanwords and modern international names adopted into Irish usage.

Consider related options instead of strict Z-initial Gaelic names. Consult modern names used in Ireland that start with Z (for example Zoe or Zara) if you accept non‑Gaelic origins. Explore Irish names that produce a similar sound (names beginning with S or Si with a soft “sh” sound), or look at anglicised forms and well‑documented mythological names that can be adapted. Consult the cited authoritative sources for verified Irish names and pronunciations when widening the criteria.