How to have two lines in fancyhdr
EDIT
If I were doing this, I would consider two options.
Option 1
If you are printing double-sided, put the chapter on even pages and the section on odd pages. For example:
\documentclass[12pt,a4paper,twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage[headheight=14pt]{geometry}% don't set these manually but, if you do, you need to ensure that you change the layout dimensions consistently e.g. if headheight is bigger, what else are you going to make smaller to compensate? geometry does this automagically
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{2pt}
\fancyhf[lh,rh,ch]{}
\fancyhf[leh]{\leftmark}
\fancyhf[roh]{\rightmark}
\begin{document}
\chapter{A VERY VERY VERY LONG CHAPTER NAME}
\section{ALSO VERY LONG CHAPTER NAME}
Some text...
\newpage
\section{ANOTHER SECTION}
Some text...
\newpage
More text.
\end{document}
Option 2
[Can be combined with Option 1 if desired.]
Use a shorter version of the chapter or section title for the running headers:
\documentclass[12pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage[headheight=14pt]{geometry}% don't set these manually but, if you do, you need to ensure that you change the layout dimensions consistently e.g. if headheight is bigger, what else are you going to make smaller to compensate? geometry does this automagically
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{2pt}
\fancyhf[lh,rh,ch]{}
\fancyhf[lh]{\leftmark}
\fancyhf[rh]{\rightmark}
\begin{document}
\chapter[Shortened Long Name]{A VERY VERY VERY LONG CHAPTER NAME}
\section[Abbreviated Name]{ALSO VERY LONG CHAPTER NAME}
Some text...
\newpage
\section{ANOTHER SECTION}
Some text...
\newpage
More text.
\end{document}
Notes
Whichever approach you choose, you should not specify the content of the section and chapter titles in all caps. They will be in caps in the running headers anyway by default. If you need them in caps for the actual section and chapter titles, then customise the format of these sectional headings appropriately. titlesec is one popular package for doing this.
For example:
\documentclass[12pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage[headheight=14pt]{geometry}% don't set these manually but, if you do, you need to ensure that you change the layout dimensions consistently e.g. if headheight is bigger, what else are you going to make smaller to compensate? geometry does this automagically
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{2pt}
\fancyhf[lh,rh,ch]{}
\fancyhf[lh]{\leftmark}
\fancyhf[rh]{\rightmark}
\usepackage[uppercase]{titlesec}
\begin{document}
\chapter[Shortened Long Name]{A Very Very Very Long Chapter Name}
\section[Abbreviated Name]{Also Very Long Chapter Name}
Some text..
\end{document}
produces
Original Answer
Note that I do not recommend this. I think there are far better responses to this problem. However, if you must, you can.
Don't change layout dimensions manually. If you do, you need to make sure everything still adds up to a reasonable layout. If the header height is increased, do you really want all of the additional space to come from the bottom margin? geometry will do something more sensible...
You need a header height of at least 28pt for this - 26pt is insufficient.
\documentclass[12pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage[headheight=28pt]{geometry}% don't set these manually but, if you do, you need to ensure that you change the layout dimensions consistently e.g. if headheight is bigger, what else are you going to make smaller to compensate? geometry does this automagically
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\headrulewidth}{2pt}
\fancyhf[lh,rh,ch]{}
\fancyhf[lh]{\begin{minipage}[b]{\textwidth}\raggedright\leftmark\\\rightmark\\\end{minipage}}
\begin{document}
\chapter{A VERY VERY VERY LONG CHAPTER NAME}
\section{ALSO VERY LONG CHAPTER NAME}
Some text...
\newpage
\section{ANOTHER SECTION}
Some text...
\end{document}
Much more simple:
just add \markboth after the chapter or section:
\documentclass[12pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage{fancyhdr} % Header
\pagestyle{fancy}
\setlength\headheight{27.06pt}
\renewcommand{\headrulewidth}{2pt}
\begin{document}
\chapter{A VERY VERY VERY LONG CHAPTER NAME}
\markboth{A VERY VERY LONG \\ CHAPTER NAME}{}
\section{ALSO VERY LONG CHAPTER NAME}
Some text...
\newpage
\section{ANOTHER SECTION}
Some text...
\end{document}
I think this was your original idea:
