Pham tested positive for the disease this weekend, making her the first person to contract Ebola within the United States. Pham was identified by family members who confirmed her name to ABC News affiliate WFAA.
The family told WFAA that Pham, 26, graduated from Texas Christian University's nursing program in 2010.
Dr. Thomas Frieden, the director of the Centers for Disease Control and Prevention, said that Pham is in stable condition, but may not be the only person that became infected while treating Duncan.
"We have to consider the possibility that there are other cases," Frieden said Monday.
"Unfortunately [I] would not be surprised if we did see additional cases among the health care workers who treated the index patient," he said referring to Duncan.
Sources close to Dr. Kent Brantly, who survived after being infected with Ebola while doing missionary work in Liberia, told ABC News that Brantly was asked by Texas Health Presbyterian Hospital in Dallas if he would donate his blood to be used to help Pham, and he donated Sunday.
The hospital had also asked for Brantly's help when they treated Duncan, but because he was not a match, no donation took place, the source told ABC News.
Frieden said the other members of the team that treated Duncan at Texas Health Presbyterian are being closely monitored, and health officials are tracking Pham's contacts since her symptoms appeared. Freiden said there appeared to be only one person who was in contact with Pham once she became infectious.
"Stopping Ebola is hard," Frieden said.
He said because of the infection of a health care worker who was following CDC guidelines, “We have to rethink the way that we address Ebola infection control."
Frieden said an initial cleaning of Pham's apartment has been completed, but additional cleaning services will be provided today.
Dallas County Judge Clay Jenkins' office confirmed earlier today that the nurse's dog remains in the apartment. Water and food have been delivered for the dog, a King Charles spaniel, and authorities are developing a longer-term plan for how to deal with the dog while its owner is being treated.
"If that dog has to be the boy in a plastic bubble... We are going to take good care of that dog," Jenkins said.
Jenkins said the dog would not be euthanized. A dog named Excalibur that belonged to a Spanish nurse with Ebola was destroyed despite a worldwide outcry.
ABC News' John Santucci contributed to this report.