Reference to enumerate item with manually set label

You could define it like this:

\documentclass{article}
\usepackage{enumitem}
\makeatletter
\newcommand{\mylabel}[2]{#2\def\@currentlabel{#2}\label{#1}}
\makeatother
\begin{document}
\begin{enumerate}[label=\textnormal{(\arabic*)}]
    \item text1\label{itm:1}.
    \item text2\label{itm:2}.
    \item[\mylabel{itm:2b}{(2')}] manually different label.
    \item text3\label{itm:3}.
\end{enumerate}
Referencing to \ref{itm:1}\ref{itm:2}\ref{itm:2b}\ref{itm:3}.

\end{document}

If one is using hyperref, the easiest way to print the prime and have a link pointing to the right item is to modify slightly the solution by Ambika Vanchinathan by adding a dummy counter (that is, adding \newcounter{dummy} in the preamble and \refstepcounter{dummy} inside the definition of \mylabel).

However, personally I would rather redefine \item (instead of \label) through:

\makeatletter
\newcommand\myitem[1][]{\item[#1]\refstepcounter{dummy}\def\@currentlabel{#1}}
\makeatother

With this definition, manual-labeled items should be introduced as

\myitem[(2')]\label{itm:2b}

That is, changes are minimal with respect to the usual way of introducing things, so that the new definition is easier to remember. I would also define a math-mode prime through

\newcommand*{\mprime}{\ensuremath{'}}

Complete MWE:

\documentclass{article}
\newcounter{dummy}
\usepackage{hyperref}
\usepackage{enumitem}
\makeatletter
\newcommand\myitem[1][]{\item[#1]\refstepcounter{dummy}\def\@currentlabel{#1}}
\makeatother
\newcommand*{\mprime}{\ensuremath{'}}

\begin{document}
\begin{enumerate}[label=\textnormal{(\arabic*)}]
    \item text1\label{itm:1}.
    \item text2\label{itm:2}.
    \myitem[(2\mprime)]\label{itm:2b} manually different label.
    \item text3\label{itm:3}.
\end{enumerate}
Referencing to \ref{itm:1}\ref{itm:2}\ref{itm:2b}\ref{itm:3}.

\end{document}