Johnson returned to work Monday after spending days in intensive care for the virus in April. Symonds gave birth to their baby boy at University College London Hospital days later.
Symonds wrote Saturday in a private Instagram post that their son's second middle name, Nicholas, is a tribute to "Dr. Nick Price and Dr. Nick Hart -- the two doctors that saved Boris' life last month."
"Thank you so much, so much to the incredible [National Health Service] maternity team at UCLH that looked after us so well," Symonds added. "I couldn't be happier. My heart is full."
The baby's full name is Wilfred Lawrie Nicholas Johnson.
Symonds said the first name, Wilfred, is the name of the prime minister's paternal grandfather, and the first middle name, Lawrie, is after her grandfather.
Johnson was the first head of government to announce testing positive for COVID-19 back in March.