I'm going to support Hive, and I hope that the SteemPeak team does as well. I'd love to see you on there, and would support you.
As for the name, I personally find anything with "d" slapped in front of it a bit stupid & overused ( I should know, I made a project with that naming structure myself lol ). It just sounds kinda corny & lame tbh. Out of the options you provided, I personally find Peak.network the most appalling. After all, if your plan is to support multiple chains, then having "network" in the name would make a lot of sense.
The idea would be this is the "peak" of social experiences. A "network" of community hubs & spaces. I really like the sound of that!
Here's hoping I see you all on Hive :^)