I chose and proposed the name Personal Finance & Money in my original Area 51 definition for this site for one simple reason: the name we had under the Stack Exchange "1.0" model, prior to the "2.0" changes, was Basically Money. Keeping "Money" was a tip of the hat, continuity, w.r.t. the site's original brand.
While I'm talking about the original name, the "Basically" part was meant to indicate the site's general goal to help people be financially literate, being the basics needed to manage one's own finances and investments—i.e. not a site for quants or pro traders ("it is my day job") type questions, not for corporate finance (beyond what retail investors would want to know for investing, or self-employed individuals operating as a corp), not for academia. But those restrictions were never spelled out. Early on, I cared more about getting questions and building a community, and less about corralling the topics.
Then, having to later go through the Area 51 site definition process under the evolved SE 2.0 model forced me to think more about what the site should really be about, and I decided the laser focus and root name needed to reflect personal finance (including what I think of as household & family finance) as the umbrella over other topics. I didn't want the proposal to fail for lack of clarity on this! The original site was loose (e.g. economics was never explicitly off-topic) because I didn't have to gain community support for launching—I owned it. But for SE 2.0, I had to convince people to support the concept, so there needed to be a firm-enough concept to support.
But at the same time, I also wanted the "& Money" in the name, following "Personal Finance", to help transition the existing brand and community into the new SE 2.0 world. "Basically Money? Yeah, that site has become the new [Personal Finance &] Money site under stackexchange.com." That was my thinking.
So "Money" is baggage, from the past. Baggage is all. By itself, it is a vestige, not intended to be defining. This definition plus community-driven meta evolution since are what define us.
Back to the present
IMHO, we'll always have the "money" in our URL
money.stackexchange.com. I don't see any reasonable way of replacing that without upsetting a lot. And even if it could be done, I like the mnemonic. (Consider how Home Improvement has the URL
Yet, three years later, if taking the word "Money" out of the full English site name, and the logo, would alleviate some confusion and sharpen the focus that had been intended, then I'm in favour of doing that. But please keep the main URL as-is.
However, without "Money" in the name, the URL might not be as memorable to new users who would only see this site referred to as "Personal Finance".
Let's do it. It would also be advisable for Stack Exchange Inc., coincident with removing the "& Money" part, to also add a domain name alias for the site:
personalfinance.stackexchange.com should be added as a permanent redirect (301) to the existing
money.* domain name.
Your thoughts and opinions are welcome. You folks govern this place now :)