Yes, the name and email address that appears in the From field of your emails are important. Recipient mail servers their anti-spam filters "score" senders as a way of identifying reputable senders. As such, your earned reputation resets every time you change your identifying name/email address.
Be sure that the domain of your email address in the From field is consistent with the domains you used for email authentication.
To improve your reputation with recipient mail servers, it's important that you send emails from an address that you monitor for replies. When your recipients respond to your emails and interact with you, this signals to servers that you're a legitimate entity. This increases the likelihood that your emails end up delivered.
Here's an example of a good name/email address combination for the From field:
"My Product | My Company" <email@example.com>
Here's an example of a bad name/email address combination for the From field:
"No Reply" <firstname.lastname@example.org>