Why are stadiums given names of large companies but mostly paid for by the tax payer to be built?

I believe it is because those companies pay a large sum of money for naming rights that helps offset the cost of construction. Like in Philadelphia, naming rights were sold in June 2002 to the Lincoln Financial Group, for a sum of $139.6 million over 21 years. Together, the City of Philadelphia and the State of Pennsylvania contributed approximately $188 million to the stadium construction. Additional construction funding was raised from the sale of Stadium Builder's Licenses to Eagles season ticket holders.

I got that information from Wikipedia.

I guess every stadium should really be named, “tax-payer stadium”, sounds like fun.

Where else are the owners and athlete going to make their many millions if the taxpayers don't build them these stadiums?

Yep I can't remember when Miller Park was built but the naming rights were up for bid this year. American Family Insurance now bought the naming rights. Don't know if the name changes next year or the year after.

A Cherokee casino about 75 miles away just paid a huge chunk for naming rights of our civic center. They will also pay a lesser amount every year to keep it.