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How can I increase the spacing between name and the address in LaTeX class moderncv, style banking?

You need to change the command makehead to get a bigger space between name and addess with the following patch in the preamble. Change the number in \[0.5cm] for your needs. Please see that this patch is for class moderncv, version 2.0.0, the current one:

makeatletter

patchcmd{makehead}{%search

    ifthenelse{equal{@title}{}}{}{titlestyle{~|~@title}}\%

    }{%replace

    ifthenelse{equal{@title}{}}{}{titlestyle{~|~@title}}\[0.5cm]%

  }{%success

  }{%failure

  }

makeatother

With the complete MWE, based on the template of class moderncv

documentclass[11pt,a4paper,sans]{moderncv}



moderncvstyle{banking} % classic banking

moderncvcolor{blue}



usepackage[utf8]{inputenc}



usepackage[scale=0.75]{geometry}



makeatletter

patchcmd{makehead}{%search

    ifthenelse{equal{@title}{}}{}{titlestyle{~|~@title}}\%

    }{%replace

    ifthenelse{equal{@title}{}}{}{titlestyle{~|~@title}}\[0.5cm]%

  }{%success

  }{%failure

  }

makeatother



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}

photo[64pt][0.4pt]{example-image-a}

quote{Some quote}



setlength{footskip}{66pt}





begin{document}



makecvtitle



section{Education}

cventry{year--year}{Degree}{Institution}{City}{textit{Grade}}{Description}  % 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 1newline{}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 1item Person 2item Person 3end{itemize}}

  cvcolumn{Category 2}{Amongst others:begin{itemize}item Person 1, anditem Person 2end{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}





clearpage

%-----       letter       ---------------------------------------------------------

% recipient data

recipient{Company Recruitment team}{Company, Inc.\123 somestreet\some city}

date{January 01, 1984}

opening{Dear Sir or Madam,}

closing{Yours faithfully,}

enclosure[Attached]{curriculum vitae{}}

makelettertitle



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Albert Einstein discovered that $e=mc^2$ in 1905.



[ e=lim_{n to infty} left(1+frac{1}{n}right)^n ]



makeletterclosing



end{document} 

you get the following result: