Two companies submitted bids for the naming rights to Miyagi Municipal Stadium. Miyagi Prefecture is looking for a company that can pay 200 million yen or more a year for three or more years, beginning in January 1, 2014. Rakuten Eagles' the parent company Rakuten was one of the two companies and is reportedly the front-runner (bids from both companies were at or above the requirements). A decision will be finalized before the end of the year.
[UPDATE 12/15 @ 7:37pm]
Rakuten may have won naming rights to Miyagi Stadium for 210 million yen a year. The new stadium could be named Rakuten kobo Stadium.
[UPDATE 12/16 @ 3:58pm]
According to ZakZak, of the 200 million yen Nippon Seishi paid for naming rights to Miyagi Stadium every year, three-quarters went to the Eagles. They might end up losing that money if Rakuten wins the bid.
Source: ZakZak 12/16/2013