I've been assuming WebM is "web movie" and WebP is "web picture".
Someone said they thought P in WebP is for "predictive". I don't think so.
VP8 uses (as do other video codecs) P-frames, predictive or predicted frames which are deltas to the frames before them, and I-frames, intra frames, which are complete images. VP8 does not have bidirectional B-frames. I guess this is where "P is for 'predictive' " came from, but WebP does not use P-frames, WebP is based on VP8 I-frames.
Maybe the P comes from the P in VP8? I have not been able to find an explanation for what VP3/4/5/6/7/8/9 stands for.
The announcement, the documentation, the Wikipedia article, neither of them explains the WebP name.