My reaction is to recognize that Fortune is a foreign (non-Latin) name and should thus be pronounced according to the original language, if you happen to know it.
This is no different from pronouncing a French or Italian name in English according to the original pronunciation; not all will recognize the language and can apply its pronunciation, but some will.
The fact that a case ending or a derivative suffix is attached should not keep us from endeavoring to pronounce the names correctly.
I should mention that it is not unusual that despite everyone's best intentions, many anglophones butcher Finnish names beyond my recognition.
Similarly I would advice against butchering an English name by taking an overly Latin point of view.
A Latinized form of a name is another matter altogether, but that does not seem to be the case here.
I don't know whether there is a clear standard for this, but I would consider it unwise not to follow the English pronunciation of the English name and then add the Latin case ending.
Stress is best placed where it goes in the original English — if the original stress is too far, perhaps a secondary stress can be added near the end to make the end more Latin-spirited.
As a speaker of Finnish I can assure you that adoption of foreign names into a strongly agglutinative language can lead to a mess in writing or pronunciation or both.
Hard rules that work naturally for all foreign names are rare.