Hi there @CHammond!
Don here from Shopify. :)
Presuming your store's password page has been disabled, Google (and other search engines) will eventually crawl your site again and pick up and reflect the new info you added there.
If you don't want to wait for this to occur by itself again, you can request a recrawl from Google by following the steps outlined here on their support site.
Had you changed this info as part of a change to your business itself, or was this more a cosmetic change you made?
Hi again @CHammond!
Don from Shopify once again. :)
I had a look around online to try to find info on this for you from Google but have not been able to get a different answer.
The only third-party source I could find with a timeframe stated that it can be as little as 4 days or as much as 6 months.
We really just can't say for sure from here in Shopify how long a third-party service like Google might take to perform such actions.
If you are unwilling to wait for this to occur by itself, you can use the link given above to request a re-crawl from Google directly.