When Bedrock Data is looking for a matching Company across systems for this type of mapping, we are going off of the official Company level fields for the Company Name. We have specific rules in place to accommodate for slight differences in the names within each system in order to find matching companies for deduplication purposes.
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Make sure to deactivate the setting that auto-creates companies based on a contacts email address. Find this by going to Contact Settings under the Contact tab and then click on Company Properties in the left hand side bar. At the top you'll find this setting that you'll want to turn off when using the Bedrock Data integration for creating and updating companies.