Can I perform Chaturthi Shradh for ancestors whose names I do not know?

Yes. When names are unknown (as is common for the great-great-grandfather generation), the sankalpa uses the phrase ‘nama-gotra ajnata’ (name and gotra unknown) and directs the offering to ‘all ancestors of the paternal lineage up to the fourth generation.’ The intent and the correct Vedic procedure are what ensure the offering reaches its destination.