Kingdom sounds good, only for other reasons than what it traditionally implies (or whatever that means in regard to governmental structure). Kingdom in name is simply... more "unique." But then again, I agree it has bad historical connotations. And Kingdoms exists solely because of such historical legacies (of which Asgardia is absent, and I think it's good to keep it that way, because we don't want them to mess with Asgardian identity). Only an alternative... Republic? Commonwealth? Excuse me, but I thought Asgardia was trying to create something new and the connotation of "republic" is pretty vanilla. It doesn't really serve as announcement "Asgardia is supposed to be different" "it's a space nation where all people are welcome" or "we don't want to be involved in your usual conflicts, we want to lead as an example of one humanity"
We want to be recognized as an equal nation by other countries and people usually avoid "weird" "new" things - so obviously can't come up with anything too fancy and weird sounding - but I would rather see the name changed into something better, something new, something "unique." Helps to send a message. A psychological threshold of a sort. Someone hears about Asgardia and then wonders about its full name "ah, that's so different, never heard of it!" Makes people more interested. If done right, can even bring prestige of a sort. Nothing comes to my mind right now but basically: use a new word that hasn't really been used before.
You people are really focused on what's written in the constitution and want to change everything right away (which I apploud, since you come up with so many ideas in detail) but there is one thing I think is important to note... Asgardia isn't really functioning yet. And frankly, I don't mean the government (which is also the case), but the identity of Asgardians. How can you state morality and philosophy and other similar things in the constitution when we haven't even seen yet what moves Asgardian citizens...? What worldviews and new Asgardian philosophy are they willing to adopt on top of their native ones? How can this influence the terminology that you can then use in the constitution? (in order to make things more clear, that is). I don't think you can make the constitution perfect at this point and there WILL BE ALWAYS a loophole of some sort, if someone wants to find it. Especially in regard to morality, minority treatment and some form of prosecution, cenzorship. Sometimes all it takes is just... one word. Presented in a different light or context that doesn't really exist yet (hence can't be prevented) and may arise 50 years from now, for all we know... Let's make it efficient people. Don't repeat mistakes of the past. Arguing over stuff that has no utilization (as of now) and making changes that do not serve anybody except our own grande of idealism. Let's keep the focus on nation's growth (including more exposure and consolidation of Asgardian identity, which is yet to take basic roots), economic growth/sustainability, and other pragmatic things like establishing the government and updating the lines that really are in need of rapid fixing.