This is very interesting, indeed. I have copies of my great-grandparents (Obereiner/Rejterew) in which the names are written in 2 languages. One, I'm told, is Polish and the other German. I will need to pull them out and find the name of the church. Her name Rejterew apparently included some naming convention to indicate she is the daughter of 'Rejter?'. I understand the concept, such as adding 'son' to one's name to idenify their son. I don't know how this was done in Polish.
Yes, there is a rumor the Gutzats were in Lithuania at some point.