Understandable confusion, I've seen it referred to both ways. We decided to go with BPF for this blog post since that appears to be the official abbreviation.
From "BPF Performance Tools" by Brendan Gregg:
"Extended BPF is often abbreviated as eBPF, but the official abbreviation is still BPF, without the "e," so throughout this book I use BPF to refer to extended BPF. The kernel contains only one execution engine, BPF (extended BPF), which runs both extended BPF and "classic" BPF programs."
From "BPF Performance Tools" by Brendan Gregg:
"Extended BPF is often abbreviated as eBPF, but the official abbreviation is still BPF, without the "e," so throughout this book I use BPF to refer to extended BPF. The kernel contains only one execution engine, BPF (extended BPF), which runs both extended BPF and "classic" BPF programs."