Unless they are asking you to divulge your social security number or like sensitive/secure information, your employer is within its rights to ask you to do so. That is unless this runs counter to an employment contract or union agreement, or is based on some form of workplace discrimination. Absent that your employer is within its legal rights. In most cases the majority of employment arrangements are what is known as "at will". Therefore, an employer can hire or fire someone for any reason or no reason at all, as well has increase/decrease salary/hours, promote/demote, and generally impose requirements as it sees fit. This includes putting personal information about your self on your name badge. In turn, an employer can work for an employer or not, their choice.