Here's one possible solution using thmtools
as a front-end for amsthm
:
\documentclass{article}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage{lipsum}
\declaretheoremstyle[
spaceabove=\topsep, spacebelow=\topsep,
headfont=\normalfont\bfseries,
notefont=\bfseries, notebraces={}{},
bodyfont=\normalfont\itshape,
postheadspace=0.5em,
name={\ignorespaces},
numbered=no,
headpunct=:]
{mystyle}
\declaretheorem[style=mystyle]{named}
\begin{document}
\begin{named}[NAME]
\lipsum[4]
\end{named}
\begin{named}[OTHERNAME]
\lipsum[4]
\end{named}
\end{document}

And without using thmtools
, you can say something like:
\documentclass{article}
\usepackage{amsthm}
\usepackage{lipsum}
\makeatletter
\newtheoremstyle{mystyle}%
{\topsep}{\topsep}
{\itshape}{}
{\bfseries}{:}
{0.5em}
{\thmname{\@ifempty{#3}{#1}\@ifnotempty{#3}{\MakeUppercase{#3}}}}
\makeatother
\theoremstyle{mystyle}
\newtheorem*{named}{NAME}% here the second argument is the default name
\begin{document}
\begin{named}
\lipsum[4]
\end{named}
\begin{named}[Othername]
\lipsum[4]
\end{named}
\end{document}

With the second approach, you can set the default name for the structure in the second argument of \newtheorem*
.