I have found this name on a Finnish woman; it has been used on around 111 women in Finland. It isn't in the Finnish name calendar, nor on this database as a Finnish name; the only thing I can find is its use as a Finnish male name on nordicnames.de.
Seeing as how Mann and Manni are, apparently, Estonian variants on Maria, would it be correct to assume that this is also a Finnish variant on Maria? Or does it have a separate origin?
Links:Finnish name statistics for Manna: http://verkkopalvelu.vrk.fi/Nimipalvelu/default.asp?L=3
Mann: https://www.behindthename.com/name/mann/submitted
Manni: https://www.behindthename.com/name/manni/submitted
Manna as a male Finnish name: https://www.nordicnames.de/wiki/Manna_m