The name Carstenius is a Latin derivate (for a priest) of the name Carstens which originates in Lübeck, Germany, in the 17th century or earlier.
During the centuries, the name has undergone a number of changes resulting in variations, the most common of which probably are Carsten and Karsten.
The families Carstens have spread all over the world from Lübeck, and given that the name "Carsten" may refer to "Christ" or "cross", there may be more families Carsten than now recognized. From the family originating in Lübeck, two major branches are known having emigrated mainly, but not restricted to Finland and Denmark.
The first Carstenius, however, may be XI Bishop of Viipuri, Finland (currently occupied by the Russians) Henric Carstenius.
For those interested in the name Carstens or any given variates of it, please see Project Carsten.