Well, the header you wants can be rebuild by using the header of style classic (and not casual as you mentioned).
In this case simple do not add an photo to your cv (or comment the existing one) and call the header before begining the document in style banking with
\moderncvhead{1} % Head of classic style % <=========================
So with the following MWE
\documentclass[11pt,a4paper,sans]{moderncv}
% moderncv themes
\moderncvstyle{banking} % casual, classic, banking, oldstyle and fancy
\moderncvcolor{blue}
\usepackage[utf8]{inputenc}
\usepackage[scale=0.75]{geometry}
% personal data
\name{John}{Doe}
\title{Resumé title}
\address{street and number}{postcode city}{country}
\phone[mobile]{+1~(234)~567~890}
\phone[fixed]{+2~(345)~678~901}
\phone[fax]{+3~(456)~789~012}
\email{john@doe.org}
\homepage{www.johndoe.com}
\social[linkedin]{john.doe}
\social[twitter]{jdoe}
\social[github]{jdoe}
\extrainfo{additional information}
%\photo[64pt][0.4pt]{example-image-a} % <===============================
\quote{Some quote}
\setlength{\footskip}{66pt}
\moderncvhead{1} % Head of classic style % <=========================
\begin{document}
\makecvtitle
\section{Education}
\cventry{year--year}{Degree}{Institution--3}{City--4}{\textit{Grade}--5}{Description--6} % arguments 3 to 6 can be left empty
\cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description}
\section{Master thesis}
\cvitem{title}{\emph{Title}}
\cvitem{supervisors}{Supervisors}
\cvitem{description}{Short thesis abstract}
\section{Experience}
\subsection{Vocational}
\cventry{year--year}{Job title}{Employer}{City}{}{General description
no longer than 1--2 lines.\newline{}%
Detailed achievements:%
\begin{itemize}%
\item Achievement 1;
\item Achievement 2, with sub-achievements:
\begin{itemize}%
\item Sub-achievement (a);
\item Sub-achievement (b), with sub-sub-achievements (don't do this!);
\begin{itemize}
\item Sub-sub-achievement i;
\item Sub-sub-achievement ii;
\item Sub-sub-achievement iii;
\end{itemize}
\item Sub-achievement (c);
\end{itemize}
\item Achievement 3.
\end{itemize}}
\cventry{year--year}{Job title}{Employer}{City}{}{Description
line 1\newline{}Description line 2}
\subsection{Miscellaneous}
\cventry{year--year}{Job title}{Employer}{City}{}{Description}
\section{Languages}
\cvitemwithcomment{Language 1}{Skill level}{Comment}
\cvitemwithcomment{\textbf{Language} 2}{\textbf{Skill} level}{Comment}
\cvitemwithcomment{Language 3}{Skill level}{Comment}
\section{Computer skills}
\cvdoubleitem{category 1}{XXX, YYY, ZZZ}{category 4}{XXX, YYY, ZZZ}
\cvdoubleitem{category 2}{XXX, YYY, ZZZ}{category 5}{XXX, YYY, ZZZ}
\cvdoubleitem{category 3}{XXX, YYY, ZZZ}{category 6}{XXX, YYY, ZZZ}
\section{Interests}
\cvitem{hobby 1}{Description}
\cvitem{hobby 2}{Description}
\cvitem{hobby 3}{Description}
\section{Extra 1}
\cvlistitem{Item 1}
\cvlistitem{Item 2}
\cvlistitem{Item 3. This item is particularly long and therefore
normally spans over several lines. Did you notice the indentation
when the line wraps?}
\section{Extra 2}
\cvlistdoubleitem{Item 1}{Item 4}
\cvlistdoubleitem{Item 2}{Item 5}
\cvlistdoubleitem{Item 3}{Item 6. Like item 3 in the single column list before, this item is particularly long to wrap over several lines.}
\section{References}
\begin{cvcolumns}
\cvcolumn{Category 1}{\begin{itemize}\item Person 1\item Person 2\item Person 3\end{itemize}}
\cvcolumn{Category 2}{Amongst others:\begin{itemize}\item Person 1, and\item Person 2\end{itemize}(more upon request)}
\cvcolumn[0.5]{All the rest \& some more}{\textit{That} person, and \textbf{those} also (all available upon request).}
\end{cvcolumns}
\end{document}
you get the wished result:
