The counter for \endnote is stepped after the endnote text has been processed. So we have to reach in the argument to increment it beforehand in order to pass the automatically generated label to \pageref
\documentclass[oneside,10pt]{memoir}
\usepackage{endnotes} % To write endnotes
\usepackage{lipsum}
\newcommand{\addendnotepage}[1]{~page~#1: }
\newcommand{\MyEndNote}[1]{%
\expandafter\endnote\expandafter{%
\expandafter\addendnotepage\expandafter{%
\expandafter\pageref\expandafter{%
\the\numexpr\arabic{endnote}+1\relax:endnote%
}%
}%
#1%
}%
\label{\arabic{endnote}:endnote}%
}
\begin{document}
\lipsum*[1]\MyEndNote{first endnote}\lipsum[2]
\newpage
\lipsum*[3]\MyEndNote{another endnote}\lipsum[1]\MyEndNote{a third one}
\newpage
\theendnotes
\end{document}

A different implementation with the more powerful expl3 language.
\documentclass[oneside,10pt]{memoir}
\usepackage{endnotes} % To write endnotes
\usepackage{xparse} % more powerful
\usepackage{lipsum}
\ExplSyntaxOn
\NewDocumentCommand{\MyEndNote}{m}
{
\polyv_myendnote:nf { #1 } { \int_eval:n { \arabic{endnote}+1 } }
}
\cs_new_protected:Nn \polyv_myendnote:nn
{
\endnote{\nobreakspace page \nobreakspace \pageref{#2:endnote}:~#1}
\label{\arabic{endnote}:endnote}
}
\cs_generate_variant:Nn \polyv_myendnote:nn { nf }
\ExplSyntaxOff
\begin{document}
\lipsum*[1]\MyEndNote{first endnote}\lipsum[2]
\newpage
\lipsum*[3]\MyEndNote{another endnote}\lipsum[1]\MyEndNote{a third one}
\newpage
\theendnotes
\end{document}
This is much more flexible; for instance, if you change the definition of \polyv_myendnote:nn into
\cs_new_protected:Nn \polyv_myendnote:nn
{
\endnote{#1\nobreakspace(page\nobreakspace\pageref{#2:endnote})}
\label{\arabic{endnote}:endnote}
}
with no other change, you'd get

With the f variant, the second argument to \polyv_myendnote:nf is expanded prior LaTeX passes it to the main function \polyv_myendnote:nn.
Page 3. 3. third 4. fourth Page 4: X. and so on
It would need to modify the code of the command \theendnotes, right ?
– PolyV Jul 01 '18 at 08:44.entfile. – egreg Jul 01 '18 at 09:08