looking to map (for example) all the various Kroger brand store names to "Kroger", will appreciate any pointers to datasets and/or data scrubbing logic.
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It depends on your budget. I'd assume you need free data.
A good start will be Croctail, they also provide API and bulk download. Mind that the data there, cleaned and parsed from SEC EDGAR's filings maps a legal entity to another legal entity relationship - you'll see relationship between the different Kroger companies, which might in term be operating some local stores.
Alternatively, you can query Unigraph which incorporates data from various sources including SEC EDGAR. With this query you can get a list of all companies (not individual stores) owned by Kroger.
Disclaimer: I'm building Unigraph, reach out for more information or API key
If you can pay for the data, Factual will be a great choice, here's what they have on Kroger.
they have store Names and lat/long...