Your server name does not match the certificate name. The third line below is the clue. I’m afraid I do not know how to help further but it’s definitely an SSL name matching issue.
SSL_connect:before/connect initialization
SSL_connect:SSLv2/v3 write client hello A
SSL3 alert read:warning:unrecognized name
SSL_connect:SSLv3 read server hello A
depth=3 C = US, O = "The Go Daddy Group, Inc.", OU = Go Daddy Class 2 Certification Authority
verify return:1
depth=2 C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", CN = Go Daddy Root Certificate Authority - G2
verify return:1
depth=1 C = US, ST = Arizona, L = Scottsdale, O = "GoDaddy.com, Inc.", OU = http://certs.godaddy.com/repository/, CN = Go Daddy Secure Certificate Authority - G2
verify return:1
depth=0 OU = Domain Control Validated, CN = jasonbarnettephotography.com
verify return:1
SSL_connect:SSLv3 read server certificate A
SSL_connect:SSLv3 read server key exchange A
SSL_connect:SSLv3 read server done A
SSL_connect:SSLv3 write client key exchange A
SSL_connect:SSLv3 write change cipher spec A
SSL_connect:SSLv3 write finished A
SSL_connect:SSLv3 flush data
SSL_connect:SSLv3 read server session ticket A
SSL_connect:SSLv3 read finished A