What is the correct name for the “>” command

> is a redirection operator. Note that using > to redirect to a regular file will overwrite what is already there, unless noclobber is set. >> will append to the end of the file.

> redirects output to a file (or device) overwriting anything already existing there

>> redirects output to a file (or device) appending to anything already existing there

< directs data from a file (or device) to a program or device

<< directs new data from a file (or device) to a program or device

As other people have answered, > is not a command, but rather a redirect operator. However, the term 'redirection operator' doesn't specifically refer to the >, but a number of different possible redirection operators. The dash man page lists the following as redirection operators:

 < > >| << >> <& >& <<- <>

I'm not sure there is a valid individual name for each one. Maybe if you dig through some old shell manuals you will find something interesting. This source, correct or incorrect, certainly has a go at naming some of them:

>  - 'output redirection operator'
<  - 'input redirection operator'
>> - 'output append operator'

But also:

2> - 'standard error redirection operator'

However I don't think this is really correct since the 2 is technically an argument rather than part of the operator.

A quick reference (in case you don't recognise any of the ones above):

>   - redirect output stream to a file, eg >somefile (for stdout) or 2>somefile
>|  - as above but overwrite the file even if the noclobber shell option is set
>>  - append output stream to file
<   - redirect input stream from file, n defaults to 0 for stdin
<>  - open file for reading and writing on stdin
>&  - redirect output stream to another stream (eg >&1) or close with - (eg 2>&-)
<<  - here document - see http://en.wikipedia.org/wiki/Here_document
<<- - here document with leading tabs removed.

In bash you also have:

<<< - here string, a one line here file. Eg <<<"foo bar"