documentclass{article}
begin{document}
newcommandrnumber{mathop{mbox{$r$-$mathit{number}$}}}
[
rnumber(5) = 120
]
end{document}

documentclass{article}
usepackage{amsmath}
mathchardefmhyphen="2D % Define a "math hyphen"
begin{document}
newcommandrnumber{mathop{rmhyphen number}}
[
rnumber(5) = 120
]
end{document}

documentclass{article}
usepackage{amsmath}
begin{document}
newcommandrnumber{operatorname{r-number}}
[
rnumber(5) = 120
]
end{document}

documentclass{article}
usepackage{amsmath}
DeclareMathOperator{rnumber}{r-number}

% Remove the line above and use the following if
% the "r" represents a math variable
%newcommand{rnumber}{mathop{r{textnormal{-number}}}}

begin{document}
$rnumber(2)$

% Just to show the effect of the alternative definition
renewcommand{rnumber}{mathop{r{textnormal{-number}}}}
$rnumber(2)$

end{document}