\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{float}
\usepackage{newfloat}
\newtheorem{thm}{\theoremname}
\newtheorem{example}[thm]{\protect\examplename}
\providecommand{\examplename}{Example}
\DeclareFloatingEnvironment{floppy}
\begin{document}
\begin{example}
        test
\end{example}
\providecommand{\algorithmname}{Algorithm}
\floatstyle{ruled}
\newfloat{algorithm}{thp}{lop}
\floatname{algorithm}{\protect\algorithmname}
\begin{algorithm}
 test
\caption{A test algorithm}
\end{algorithm}
\newfloat{flippy}{thp}{lop}
\begin{flippy}
A Flippy!
\caption{Something that turns\label{flp}}
\end{flippy}
See the \ref{flp}.
\makeatletter
  Check: Macro flippyname \@ifundefined{flippyname}{is NOT}{IS} defined.
\makeatother  
\begin{floppy}
A Floppy!
\caption{Something that flops\label{flp2}}
\end{floppy}
See the \ref{flp2}.
\makeatletter
  Check: Macro floppyname \@ifundefined{floppyname}{is NOT}{IS} defined.
\makeatother  
\end{document}