If you have a problem when uploading images with umlauts in the file name you first stop may will be to check the config.local_all setting. The setting should match some value of the locale -a command of the server. Mose of the time it’s something like en_US.uft8 or de_DE.utf8.
But if you still getting errors like

/usr/local/bin/gm convert: Unable to open file ([image file name]) [No such file or directory].

You should also set systemLocale of the Typo3 configuration. The most simple way to do this is to use the Installation Tool/All Configuration:

$TYPO3_CONF_VARS['SYS']['systemLocale'] = 'de_DE.utf-8';