Every shipping vessel that enters and leaves the United States is required to submit shipping records that document its cargo. This information filed to Customs is called “Automated Manifest System” -> http://www.cbp.gov/trade/trade-community/automated/automated-systems/ams. Thanks to the Freedom of Information Act, most of this information is a matter of public record. There are sites (www.piers.com, www.zepol.com, www.importgenius.com) that retrieve and publish this information.
There is a way to request with Customs confidentiality. You can read instructions on the following website: https://help.cbp.gov/app/answers/detail/a_id/285/~/importers—confidential-treatment-of-vessel-manifest-data
You should include ALL variations of your company name as they may be manifested in the AMS system. Customs allows you to provide a maximum of 10 variations. Therefore you also need to work with your freight forwarders who file the AMS on your behalf to make sure that the names they use in the filing match up with the 10 variations you have requested confidentiality for.
The protection is just for future shipments and does not reflect information from prior shipments. According to the above site, the protection lasts only two years, after which time you will have to reapply.