According to Greek legend, Deianeira was the wife of Hercules who unwittingly brought about Hercules' demise by believing a lie told to her by the centaur, Nessus.
As for what the name "Deianeira" actually means... I guess we'll have to wait for Pavlos, our resident Greek etymologist, to decipher that one.
What may be of interest to you... According to the Social Security Administration's Office of the Chief Actuary, there was a total of 43 girl children born last year whose parents filed a Social Security application for them, who were given the name of "Deyanira". There were 44 girl children given the name of "Deyaneira".