Legal Question in Intellectual Property in California

It would depend upon how the expression "company resource" is defined in the working relationship between the employer and employee. I would be inclined to think that if the employee is billing not only the per-message usage charges, but also the fixed periodic cost to have the service available, then it probably becomes a "company resource" even if the account is in the employee's name. In any case, if the employee here values the business relationship with the employer, this issue should be negotiated civilly until an understanding is achieved.