General:
* Label
* Tag (this is often used interchangeably with "clothing tag")
* Ticket
* Brand tag
* Care label
* Size tag
* Wash tag
* Hangtag (for tags attached to clothes on a hanger)
More Specific:
* Fabric label (for tags that indicate the composition of the garment)
* Care instructions (for tags that explain how to wash, dry, and care for the garment)
* Size label (for tags that indicate the size of the garment)
* Country of origin tag (for tags that indicate where the garment was manufactured)
The best word to use will depend on what kind of information is on the tag and what you are trying to convey.