I can't see any reason to leave the old name in the footer, note that it's "Arqade" in the list of all sites as well.
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The new footer will be using site names.
Arqade and Mi Yodeya it is, and hovering over the name gives you a description.
We will add some overrides for specific sites, so it will be clearer what topic they belong to - so it will be "Arqade (gaming)" and "Mi Yodeya (Judaism)" and such.
No, please don't change it. The links in the footer are not site names - they are topics.
Topics are meaningful to everyone: regulars, brand new visitors, search engines.
Site names are only meaningful to regulars. And any regular who wanted Arqade, would know they wanted the gaming site anyway.
By the same rationale the following changes should also be made:
Having said that I'm in two minds about this. On the All Sites page you can click on a site and it explains what the site is about. In the footer this doesn't happen. A descriptive single word in the footer that adequately explains what the site is about may be preferable to the brand of the site itself, which is available once you navigate there anyway.