Desperate to flee the flashpoint Syrian border town, the heavily pregnant mother, her husband and six other children made it across the frontier just in time for the boy's arrival.
Islamic State (IS) jihadists, accused of widespread atrocities, seized control of the strategic locality and US-led bombing raids launched in the last few weeks have tried to stop their advance.
"Because of his help maybe we will get rid of this cruelty and get back to our homes"
"I gave my son this name from my heart. I will never change this name," the shy 35-year-old said in a refugee camp in Suruc, just inside Turkey.
"He dispatched planes, aid for us. Because of his help maybe we will get rid of this cruelty and get back to our homes," she said, cradling her three-day-old son.
The family started their exodus almost a month ago, following some 200,000 Kurds who have already entered Turkey to escape the IS onslaught on Kobane.
"We were stranded at the border for days, without water or food," said the young mother. "We did not take any clothes to wear. We did not have any blankets ... I was pregnant and had no chance of taking a bath."
Though not the world's first baby named after US President Barack Obama, the choice reflects the relief of many locals who thought help would never come.
'NO FRIENDS BUT THE AMERICANS'
"We named him Muhammed Obama Muslim," father Mahmut Beko said, in symbolic gratitude for the US assistance to save Kobane.
"We want Obama to help us so that we can get back home. We are also human beings. We, the Kurds, attacked whom, fight against whom?" he cried out.
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The family is housed at the "Rojova Cadir Kenti" refugee camp, whose name is a mix of Turkish for "tent city" and the name of the northern part of Syria.
There, joy abounds over the air strikes by a coalition of Western and Arab allies that have killed more than 500 Islamist fighters during a month-long campaign in Syria.
US planes have also dropped bundles of supplies, which include ammunitions and weapons, to help Syrian Kurdish fighters trying to defend Kobane from the IS, an extremist Sunni Muslim group that has seized control of large parts of Syria and Iraq.
Turkey, long at odds with Kurdish separatists, has criticised the air drops and officials said some of the supplies have fallen into IS hands.
"US planes have also dropped bundles of supplies"
Near Suruc, both Turkish and Syrian Kurds watch from hilltops, breaking out in cheers, whistles and chanting, "Obama, Obama" at each airstrike.
"Like the Americans, the whole world should help the Kurds in Kobane. We have no true friends other than the Americans," said Selami Altay, a Turkish Kurd, sitting on a rock watching the battles.
Sultan Muslim, meanwhile, said despite all she had an easy birth, taken by ambulance from the tent city to a hospital in Suruc. And despite the miserable conditions and uncertainty, she has dreams for her baby.
"The day will come when he grows up and becomes like him (President Obama) and saves people from cruelty.
"Nobody helped us, but him," she said.