Following Mathematica's general naming convention, function names in StandardForm are just the capitalized versions of their traditional mathematics names. This shows the cosecant function in StandardForm.
This shows the cosecant function in TraditionalForm.
Mathematica has other popular forms of notations that are used for print and electronic publications. In this particular instance the task is not difficult. However, it must be made to work in Mathematica's CForm, TeXForm, and FortranForm.