I bought a house- why is the previous owners name still on the tax bill?

The official real estate taxpayer (taxpayer of record) for any tax year(fiscal year) is the owner on January 1 of the calendar year that the tax year(fiscal year) begins. The taxpayer of record does not change over the course of that tax year(fiscal year), even if the property changes hands during that time. Although the tax bill will bear the name of the assessed owner(taxpayer of record/previous owner) as of January 1, the new owner is responsible for all taxes once the sale of the property is finalized.

For example, Owner A sells to Buyer B in June 2015. Owner A is the taxpayer of record for the entire tax year(fiscal year) from July 1, 2015 to June 30, 2016 and both real estate tax bills will be addressed to Owner A in care of Buyer B.   During the next fiscal year, Buyer B owns the property on January 1, 2016,  bills for the  tax year from July 1, 2016 to June 30, 2017 and beyond will be addressed to Buyer B.

The office of the Board of Assessors -who issue the tax bills- can mail the bill in care of the new owner at the same or a different address as long as they are notified by the new owner.  If the new owner notifies the office of the Assessors of the change, the subsequent bills will then be addressed to Owner A in care of Buyer B .