Using htop to list users. Which is one of my favourite.

% top -U user1

pstree which displays a tree of processes and can include parents and child processes which make it easier to understand.

% pstree -l -a -p -s user1

where
-l : Long format
-a : Show command line args
-p : Display Linux PIDs
-s : See parents of the selected process

pgrep look up or signal processes based on name and other attributes

% pgrep -l -u user1

References:

1. Linux list processes by user names