Read cell value from string array and it assign to macro

\readrecordarray is meant for one-dimensional arrays, but \mydata[...] is used as 2-D array.

Rather use \readdef{myfile.txt}\myfile to provide a 'data-macro' and apply \readarray\myfile\mydata[2,2] later on.

\documentclass{article}
\usepackage{readarray}[2016-11-07]
\begin{filecontents*}{myfile.txt}
Alfred; Koch
Mildred; Jane
\end{filecontents*}

\usepackage[utf8]{inputenc}
\usepackage[T2A,T1]{fontenc}
\usepackage[ukrainian]{babel}

%\usepackage{filecontents}

\begin{document}
\readarraysepchar{;}
\readdef{myfile.txt}\myfile
\readarray\myfile\mydata[2,2]

\def\Nameone{\mydata[1,1]}
\def\Nametwo{\mydata[2,1]}
\def\Surnameone{\mydata[1,2]}
\def\Surnametwo{\mydata[2,2]}


\Nameone\  \Surnameone


\Nametwo\ \Surnametwo


\end{document}

I propose an altogether different approach, which has the advantage of being “fully expandable”; for example you can even do

\MakeUppercase{\Nameone}

and it will print

ALFRED

Here is the code. The idea is to read the file line by line; each line is stored as the item of a sequence, but the internal items are transformed in the form {item1}{item2}, so they can be retrieved expandably with \tl_item:nn (in its variant form \tl_item:fn, because we first extract the row from the sequence).

\begin{filecontents*}{\jobname.dat}
Alfred; Koch
Mildred; Jane
\end{filecontents*}

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
% variables
\ior_new:N \g_kapone_array_file_stream
\tl_new:N \l_kapone_array_separator_tl

\seq_new:N \l__kapone_array_temp_seq
\tl_new:N \l__kapone_array_temp_tl

% user level commands
\NewDocumentCommand{\readarrayfile}{mm}
 {
  \seq_clear_new:c { kapone_array_#1_seq }
  \ior_open:Nn \g_kapone_array_file_stream { #2 }
  \ior_map_inline:Nn \g_kapone_array_file_stream
   {
    \kapone_array_line:nn { #1 } { ##1 }
   }
 }

\NewDocumentCommand{\arrayseparator}{m}
 {
  \tl_set:Nn \l_kapone_array_separator_tl { #1 }
 }
\arrayseparator{,} % default

\NewExpandableDocumentCommand{\arrayitem}{mmm}
 {
  \kapone_array_item:nnn { #1 } { #2 } { #3 }
 }

% lower level functions
\cs_new_protected:Nn \kapone_array_line:nn
 {
  \seq_set_split:NVn \l__kapone_array_temp_seq \l_kapone_array_separator_tl { #2 }
  \tl_clear:N \l__kapone_array_temp_tl
  \seq_map_inline:Nn \l__kapone_array_temp_seq
   {
    \tl_put_right:Nn \l__kapone_array_temp_tl { {##1} }
   }
  \seq_put_right:cV { kapone_array_#1_seq } \l__kapone_array_temp_tl
 }

\cs_new:Nn \kapone_array_item:nnn
 {
  \tl_item:fn { \seq_item:cn { kapone_array_#1_seq } { #2 } } { #3 }
 }

% variants
\cs_generate_variant:Nn \seq_set_split:Nnn { NV }
\cs_generate_variant:Nn \seq_put_right:Nn { cV }
\cs_generate_variant:Nn \tl_item:nn { f }
\ExplSyntaxOff

\begin{document}

\arrayseparator{;}
\readarrayfile{mydata}{\jobname.dat}

\newcommand{\Nameone}{\arrayitem{mydata}{1}{1}}
\newcommand{\Nametwo}{\arrayitem{mydata}{2}{1}}
\newcommand{\Surnameone}{\arrayitem{mydata}{1}{2}}
\newcommand{\Surnametwo}{\arrayitem{mydata}{2}{2}}


\Nameone

\Nametwo

\Surnameone

\Surnametwo

\edef\test{\arrayitem{mydata}{1}{1}}
\texttt{\meaning\test}

\end{document}

An extended version where one can access the number of rows and columns of an array.

\begin{filecontents*}{\jobname.dat}
Alfred; Koch
Mildred; Jane
\end{filecontents*}

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
% variables
\ior_new:N \g_kapone_array_file_stream
\tl_new:N \l_kapone_array_separator_tl

\seq_new:N \l__kapone_array_temp_seq
\tl_new:N \l__kapone_array_temp_tl

% user level commands
\NewDocumentCommand{\readarrayfile}{mm}
 {
  \seq_clear_new:c { l_kapone_array_#1_seq }
  \int_zero_new:c { l_kapone_array_cols_#1_int }
  \ior_open:Nn \g_kapone_array_file_stream { #2 }
  \ior_map_inline:Nn \g_kapone_array_file_stream
   {
    \kapone_array_line:nn { #1 } { ##1 }
   }
 }

\NewDocumentCommand{\arrayseparator}{m}
 {
  \tl_set:Nn \l_kapone_array_separator_tl { #1 }
 }
\arrayseparator{,} % default

\NewExpandableDocumentCommand{\arrayitem}{mmm}
 {
  \kapone_array_item:nnn { #1 } { #2 } { #3 }
 }

\NewExpandableDocumentCommand{\arrayrows}{m}
 {
  \seq_count:c { l_kapone_array_#1_seq }
 }
\NewExpandableDocumentCommand{\arraycols}{m}
 {
  \int_use:c { l_kapone_array_cols_#1_int }
 }

% lower level functions
\cs_new_protected:Nn \kapone_array_line:nn
 {
  \seq_set_split:NVn \l__kapone_array_temp_seq \l_kapone_array_separator_tl { #2 }
  \int_set:cn { l_kapone_array_cols_#1_int }
    {
     \int_max:nn
      { \int_use:c { l_kapone_array_cols_#1_int } }
      { \seq_count:N \l__kapone_array_temp_seq }
    }
  \tl_clear:N \l__kapone_array_temp_tl
  \seq_map_inline:Nn \l__kapone_array_temp_seq
   {
    \tl_put_right:Nn \l__kapone_array_temp_tl { {##1} }
   }
  \seq_put_right:cV { l_kapone_array_#1_seq } \l__kapone_array_temp_tl
 }

\cs_new:Nn \kapone_array_item:nnn
 {
  \tl_item:fn { \seq_item:cn { l_kapone_array_#1_seq } { #2 } } { #3 }
 }

% variants
\cs_generate_variant:Nn \seq_set_split:Nnn { NV }
\cs_generate_variant:Nn \seq_put_right:Nn { cV }
\cs_generate_variant:Nn \tl_item:nn { f }
\ExplSyntaxOff

\begin{document}

\arrayseparator{;}
\readarrayfile{mydata}{\jobname.dat}

\newcommand{\Nameone}{\arrayitem{mydata}{1}{1}}
\newcommand{\Nametwo}{\arrayitem{mydata}{2}{1}}
\newcommand{\Surnameone}{\arrayitem{mydata}{1}{2}}
\newcommand{\Surnametwo}{\arrayitem{mydata}{2}{2}}


\Nameone

\Nametwo

\Surnameone

\Surnametwo

\MakeUppercase{\Nameone}

The array \texttt{mydata} has \arrayrows{mydata} rows
and \arraycols{mydata} columns.

\edef\test{\arrayitem{mydata}{1}{1}}
\texttt{\meaning\test}

\end{document}