Alexandra and her husband Garren Givens honoured her father by naming their son after the late "Superman" star, reported E! Online.
"Alexandra Reeve Givens and Garren Givens welcomed their first child Christopher Russel Reeve Givens on June 13 in Washington DC," a representative said.
"He was named after his grandfathers on each side, two very important role models for Garren and Alexandra. The entire family is thriving during their first few weeks home," said a family spokes person.
Alexandra, 31, and Garren, 33, met at Yale and were married in 2008. She now works as a Senior Counsel in the United States Senate while Garren works in the Obama administration as the Director of the Presidential Innovation Fellows program.