What about all the SEO, Stack overflow questions, and the differentiation between the two(?) platforms?
1) It's not conflicting with anything major (Unless it does, short 4 letters names are way too common).
2) It will transfer along the URL redirections
3) Docker has enough credit and following to gather SEO on any new domain and product name that comes out
The new pages will be top links on google very quickly. No worries about that, machines are fine!
The trouble is with humans, they can't keep up. All the existing content -documentation, community, articles- will stay under the Docker name, forever splitting the knowledge and bringing confusion onto mankind.