documentclass[border=10mm]{standalone}
usepackage{tikz}
usetikzlibrary{calc,fit}
tikzset{
  % When open box is called via edge, draw a rectangle with no top:
  open box/.code={%
      pgfkeysalso{%
        to path={%
            let
            p{start}=(tikztostart),
            p{end}=(tikztotarget)
            in
            (tikztostart) -| (tikztotarget)
            (x{start},y{start}) -- (x{start},y{end})
            % Make a fitted node to get good anchors
            node[fit={(tikztostart)(tikztotarget)}, inner sep=0pt](#1){}
          }
      }
    }
}

begin{document}
  begin{tikzpicture}
    draw (0,0) edge[open box={therect}] (2,2);
    % How can this be switched with e.g:            %<---
    % draw (0,0) open box[name=therect] (2,2) %<---
    node at (therect.center){RECT!};
  end{tikzpicture}
end{document}