The code below assumes that the filenames do not contain linefeeds, spaces, tabs, single quotes, double quotes, or backslashes, and that filenames do not start with a dash. It also assumes that IFS has not been changed, because it uses while read instead of while IFS= read, and because variables are not quoted. Add setopt shwordsplit in Zsh.
i=1;while read l;do mkdir $i;mv $l $((i++));done< <(ls|xargs -n2000)
The code below assumes that filenames do not contain linefeeds and that they do not start with a dash. -n2000 takes 2000 arguments at a time and {#} is the sequence number of the job. Replace {#} with '{=$_=sprintf("%04d",$job->seq())=}' to pad numbers to four digits.
ls|parallel -n2000 mkdir {#}\;mv {} {#}
The command below assumes that filenames do not contain linefeeds. It uses the implementation of rename by Aristotle Pagaltzis which is the rename formula in Homebrew, where -p is needed to create directories, where --stdin is needed to get paths from STDIN, and where $N is the number of the file. In other implementations you can use $. or ++$::i instead of $N.
ls|rename --stdin -p 's,^,1+int(($N-1)/2000)."/",e'