2 problems...
the term "fallen" might be problematic, because "fallen" in English also stands for spiritually or morally corrupt, and I'm not sure, but I don't think the language uses "fallen" in terms of those who died in battle. Or, if they do, it's not as widely used as it is in Hebrew. The other problem is with the term martyrs. Those are usually religious characters who performed very religious acts, such as saints, usually in Christianity (although I'm sure they exist in every religion). Jews were killed for their ethnicity rather than religion (it didn't matter that many did not practice their religion). I can't imagine Holocaust memorial day being referred to in hebrew as יום הקדושים for that exact reason - the religious undertones are not always fitting. Personally, I'd go with your first suggestion, Holocaust Memorial Day. And as for Yom Hazikaron - maybe IDF Memorial day, although I have to say it sounds... I don't know, not right. Especially now that it's also dedicated to victims of terror. Hard to come up with a good definition in English. Americans just call it memorial day, but then they don't have as many as we do...