The other answers here, while mostly valid, are vastly overcomplicated. To change your user password in any WSL distribution, simply:
From inside Ubuntu (or another distribution):
wsl.exe \~ -u root -d $WSL_DISTRO_NAME -e passwd $USER
*Requires WSL Interop to be enabled.
Or from PowerShell or CMD (as a regular, non-admin user):
wsl ~ -u root -e passwd <username># Add the -d <distro_name> if not using the default distro
*Does not require WSL Interop.