Your requirements are a bit vague. The string "USER" might appear in multiple contexts. The more specific you are as to the expected line format, the better the solution.
A case senstive solutionn using native batch commands would be a bit tricky.
Here is a native batch slution that is not case sensitive. It looks for the word "USER" (case insesitive) either at the beginning of a line or after a space, followed by a space. It then skips one or more spaces (or tabs) and then writes out the next string up until space, tab, or end of line.
for /f delims^=^ eol^= %%A in ('findstr /ri /c:" USER " /c:" USER " *.txt') do (
if /i "!ln:~0,5!" equ "USER " (set "ln=!ln:~5!") else set "ln=!ln:* USER =!"
for /f %%B in ("!ln!") do if "%%B" neq "" echo %%B
Life is much better if you allow yourself to go beyond native batch commands. The following uses REPL.BAT - a hybrid JScript/batch utility that performs a regular expression search and replace on lines from stdin and writes the result to stdout. It is pure script that runs natively on any modern Windows machine from XP onward.
The script below assumes REPL.BAT is somewhere within your PATH. It looks for the word USER (case sensitive) followed by one or more whitespace characters (most likely spaces and/or tabs) and then writes out the next "string" up until another whitespace character. Chances are the regular expression could be modified as needed quite easily if you better define your requirements.
findstr USER *.log|repl ".*?:.*\bUSER\s+(\S+).*" $1 a >userNames.txt