This isn't a DripJobs issue — it happens because of how your client's email displays sender information.
DripJobs sends emails from an address like job-updates@dripjobs.com when your business doesn't have a custom domain connected. If your client already has that same email address saved as a contact under a different name (for example, if they work with another company that uses a similar or shared sending address), their other company they have worked with email will display the name they saved instead of your business name.
To fix this, ask your client to update or delete the existing contact entry tied to job-updates@dripjobs.com so their inbox displays the correct sender name. Alternatively, connecting a custom domain to your DripJobs account ensures emails are sent from your own domain, which avoids this kind of mix-up entirely.