Ioreth means "old woman" in Sindarin; iaur "old" plus feminine ending -eth. In draft, Tolkien had spelt her name Yoreth. Like "Gamling", it was specifically chosen to suit the character of the old nurse.
Sindarin
ioreth
feminine name. Old Woman
Elements
Word Gloss iaur “old, old; [N.] ancient, olden” -eth “feminine ending”
Ioreth
Ioreth
An old woman from Minas Tirith (LotR/860), her name was translated “Old Woman”, a combination of the prefixal form ior- of iaur “old” and the feminine suffix -eth (RC/579).
Conceptual Development: In Lord of the Rings drafts from the 1940s, this name first appeared as N. Yoreth (WR/386), but this was probably just a variant spelling rather than a real difference in the name.