Following the suggestion in How to change the name of document elements like "Figure", "Contents", "Bibliography", "Appendix", etc.?, you need to add the new \chaptername to the greek captions using
\addto\captionsgreek{\renewcommand*{\chaptername}{KEFALAIO}}
Here is a minimal example showing the adjustment:

\documentclass{memoir}
\usepackage[greek]{babel}
\addto\captionsgreek{\renewcommand*{\chaptername}{KEFALAIO}}
\begin{document}
\chapter{abc}
\end{document}
Alternatively, without the above approach, a delayed \renewcommand also suffices:
\AtBeginDocument{%
\renewcommand*{\chaptername}{\textKappa \textEpsilon \textPhi \textAlpha \textLambda \textAlpha \textIota \textOmicron}}