[Tex/LaTex] Positioning name of node label in tikzpicture

diagramslabelstikz-pgf

I have the following diagram:

\documentclass{article}
\usepackage{amsmath,amsfonts,graphicx}
\usepackage{algpseudocode}
\usepackage{tikz, nth}
\usetikzlibrary{arrows.meta,decorations,decorations.pathreplacing,calc,bending,positioning, chains}

\begin{document}
\begin{tikzpicture}[scale=0.6]
        \draw[thick,]  (0,8) -- (0,0) node[left] {0};
        \draw[thick,]  (0,0) -- (8,0) node[right] {8};
        \draw[thick,]  (8,8) -- (8,0) node[left] {};
        \draw[thick,]  (8,8) -- (0,8) node[left] {8};

        \draw[thick,]  (4,0) -- (4,8) node[left] {};

        \fill (1, 4) circle[radius=2.5pt] node[below]{$A$};
        \fill (2, 6) circle[radius=2.5pt] node[below]{$B$};
        \fill (3, 2) circle[radius=2.5pt] node[below]{$C$};
        \fill (4, 8) circle[radius=2.5pt] node[below]{$D$};
        \fill (7, 3) circle[radius=2.5pt] node[below]{$E$};
        \fill (6, 1) circle[radius=2.5pt] node[below]{$F$};
        \fill (5, 7) circle[radius=2.5pt] node[below]{$G$};
        \fill (3, 8) circle[radius=2.5pt] node[below]{$H$};
\end{tikzpicture}
\end{document}

How can I position the caption of the node $D$ both below and left, so that the line doesn't obscure the caption?

Best Answer

Let convert comments to an answer: Logic for positioning nodes, labels is the same as it is at naming of horizon's sides. For example: always we say south west (synonym for below left) and newer west south (= left below) ...

Regarding your MWE: see if the following more concise code of your MWE is useful to you:

\documentclass{article}
\usepackage{amsmath,amsfonts,graphicx}
\usepackage{algpseudocode}
\usepackage{tikz, nth}
\usetikzlibrary{arrows.meta,decorations,decorations.pathreplacing,calc,bending,positioning, chains}

\begin{document}
\begin{tikzpicture}[scale=0.6,
dot/.style = {circle, fill=black, inner sep=0pt, minimum size=5pt,
              node contents={}},
                    ]
\draw[thick]  (0,8)      node[left] {8}
                -- (0,0) node[left] {0}
                -- (8,0) node[right] {8}
                -- (8,8) -- cycle;
\draw[thick,]  (4,0) -- (4,8) node[left] {};

\path (1,4) node[dot,label=below:$A$];
\path (2,6) node[dot,label=below:$B$];
\path (3,2) node[dot,label=below:$C$];
\path (4,8) node[dot,label=below left:$D$];
\path (7,3) node[dot,label=below:$E$];
\path (6,1) node[dot,label=below:$F$];
\path (5,7) node[dot,label=below:$G$];
\path (3,8) node[dot,label=below:$H$];
    \end{tikzpicture}
\end{document}

enter image description here

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