Although the terms "race" and "ethnicity" are not identical, they are often used interchangeably as they both refer to a person bqackground.  The government is not interested in someone's specific genealogical details but rather is trying to research the origins of Americans in a general way.  America has been famously described as a "melting pot" and as a nation of immigrants.  Sometimes, someone such as a talk show host will state that the racial and ethnic background of Americans is changing from the traditional prevalence of Caucasians.  These kinds of statements and statistical descriptions are based mostly on census data.  Immigration is central to U.S. history all the way back to the founding of the colonies to the present, and so it is only natural that the public would be interested in the composition of our population as accurately as it can be surveyed and described.  Many people would be interested in knowing how their particular race or ethnicity is represented percentage wise in Congress, in private industry, or in different towns and cities.  The Founding Fathers did not put the census in the Constitution just for the fun of it; they intended statistical information to be made available to serve a useful political and economic purpose.

I would assume that the census form asks for the names of residents so that there is some concrete identification of each person being counted.  I don't know if the census cross-references names to check for possible duplications of the same person, but data base software could easily run that kind of a check.  The form I was sent expalins that a telephone number is asked for in case the census bureau has any questions about how the census form was filled out, something that is unclear or unintelligible, or maybe if the same person is listed on two different forms or some other puzzling replies.  The census bureau is only allowed to release statistical information.  I don't think the government is allowed to use the information collected for any other purpose than to compile and publish the statistics of the census.