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Mostly posting this to save time and heartache for whoever comes here looking for an answer, as I didn't find it here when I needed it....
We had a few global subscription lists, and found that, although non-english characters, such as the accented 'e' in Spanish, were correct in the database, they were not correctly displayed in the Sendy web interface(displaying the dreaded black diamond '?' instead). After some fumbling around, I discovered that manually changing my browser's text encoding to 'Western' caused the characters to display correctly, and this seemed to indicate that ISO-8859-1 encoding was what was needed.
I edited the php.ini file, and changed the following line:
default_charset = "UTF-8"
I switched it to:
default_charset = "ISO-8859-1"
Reloaded php-fpm, and now all names are displaying correctly. Hope that helps someone!