amsmath theorem name as argument

Question

How can I have an amsmath Theorem environment where the name of the environment is passed as an argument?

e.g.

\begin{note}[Name of the Theorem]
    Lorem ipsum dolor sit amet, consetetur sadipscing elitr,
    sed diam nonumy eirmod tempor invidunt ut labore et dolore
    magna aliquyam erat, sed diam voluptua.
\end{note}
\begin{note}[A different name]
    Lorem ipsum dolor sit amet, consetetur sadipscing elitr,
    sed diam nonumy eirmod tempor invidunt ut labore et dolore
    magna aliquyam erat, sed diam voluptua.
\end{note}

resulting in this:

Thanks in advance!

EDIT: Added a second example for clarity

Answer 1

See the tutorial about the Pythagorean theorem on this page.

You can add a theorem title using brackets:

\begin{theorem}[Pythagorean theorem]

EDIT: here is an exemple, but I am not sure that is what you are looking for.

\documentclass{report}
\usepackage{amsmath}
\newtheorem{theorem}{Theorem}
\newtheorem{theoremApple}{Apple}
\newtheorem{theoremBanana}{Banana}
\begin{document}
\begin{theorem}[Apple]
The apple is red.
\end{theorem}
\begin{theorem}[Banana]
The banana is yellow.
\end{theorem}
\begin{theoremApple}
The apple is red.
\end{theoremApple}
\begin{theoremBanana}
The banana is yellow.
\end{theoremBanana}
\begin{theoremApple}
Actually, the apple is green.
\end{theoremApple}
\end{document}

resulting in