Yes. In fact, it would be inefficient and a waste of judicial resources if the plaintiff had to get the order amended each time he/she gets a new job.
The caselaw excerpt you reproduced means that your contact would be forgiven only if it's merely a coincidence that the entity you contacted happens to be Plaintiff's employer without you knowing it beforehand. However, direct or circumstantial evidence may prove that your contact was a willful violation rather than just a mere coincidence. If evidence shows that you contacted an entity despite knowing that the entity was Plaintiff's employer, you'll be found in contempt.
In your case, the order is premised on a lawsuit which contains the employer's details and which has been served upon you. Therefore, that is sufficient proof that you knew or should have known that the entity you contact(-ed) is Plaintiff's employer. In the event that Plaintiff got a new job, direct or circumstantial evidence might help ascertaining whether or not you knew or should have known that this other entity is plaintiff's new employer.
Injunctions are not child's play. Trying to overcome a clear injunction entered against you is very likely to backfire.

