In Son of Godzilla, the ShodaiKumo's name comes from shodai (初代?), meaning first generation, and Kumo, which comes from Kumonga's Japanese name, Kumonga (クモンガ?).
In Destroy All Monsters, the SoshingekiKumo's name comes from the film's Japanese title, specifically sōshingeki (総進撃?), meaning attack of the marching [monsters], and Kumo, which comes from Kumonga's Japanese name, Kumonga (クモンガ?).
The ShodaiKumo puppet is much like the the later FinalKumo puppet. It's mostly black and gold, and its eyes are purple. It has a normal spider-like body, complete with a head section and an abdomen and a spider like face with 6 eyes. Its 8 striped legs have three points of articulation. The puppet is also known as SoshingekiKumo in Destroy All Monsters.