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Each lead can have one acquisition program. The intent is the program that brought that person into the database is given acquisition credit. In most cases you have to set the acquisition program manually either by changing the status designating the acq program in a flow step.
From a technical perspective, acquired by means you set the acquisition program to the email program.
From a philosophical perspective, an email program shouldn't generally be acquiring names. An asset on a website, or where ever the email is directing to might acquire new names but that should be set up as a different program.