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The name Zakheim probably means "Descendants of the Martyrs" in Hebrew
Probably all Zakheims are decendants of Yisrael the Martyr of Ruzhany, ABD Birzai and Zamosc
His children are called Z"K I traced to my relative Zakheim which are descendants of Yisrael and noticed that in one generation the name was changed from Z"K to Zakheim.
And In Hebrew: ז"ק = זרע קדושים זקה"ם= זרע קדושים הם
https://he.wikipedia.org/wiki/%D7%96%D7%A7%D7%94%D7%99%D7%99%D7%9D