First, get the package name if you're unsure about it, use pm list packages
and get the process id either with pidof, adb shell ps -A | grep <package-name> or top, you can use termux but you need to be root first and must use ps executable from /system/bin to fully list all running process (somehow ps executable from termux package is limited even when executed as root).
and get the log by filter its pid:
adb shell 'logcat --pid=$(pidof -s <package_name>)'
reference:
- appscms.com - android pm command
- stackoverflow.com - logcat specific app