Name of Draupadi sons
Pandavas and Draupadi had five sons, there names are mentioned in Mahabharata Adi Parva chapter 220 verse 79-85, also referred as Harnaharana Parva (हरणाहरणपर्व)
युधिष्ठिरात्प्रतिविन्ध्यं सुतसोमं वृकोदरात्।
अर्जुनाच्छ्रुतकर्माणं शतानीकं च नाकुलिम्।।
Prativindhya (प्रतिविन्ध्य) from Yudhishthira, Sutasoma (सुतसोम) from Bheema, Shrutakarma (श्रुतकर्मा) from Arjuna, Satanika (शतानीक) from Nakula and Shrutasena (श्रुतसेन) from Sahadeva.
How the name of Draupadi son are derived ?
परप्रहरणज्ञाने प्रतिविन्ध्यो भत्वयम्।।
Prativindhya (प्रतिविन्ध्य) got his name because the Brahmanas told Yudhishthira that he would be like Vindhya mountains and should not get impacted by the strike of enemies.
सुतेसोमसहस्रे तु सोमार्कसमतेजसम्।
सुतसोमं महेष्वासं सुषुवे भीमसेनतः।।
Sutasoma (सुतसोम) got his name because he was born after Bhima performed thousands of soma sacrifices.
श्रुतं कर्म महत्कृत्वा निवृत्तेन किरीटिना।
जातः पुत्रस्तथेत्येवं श्रुतकर्मा ततोऽभवत्।।
Shrutakarma (श्रुतकर्मा) got his name because किरीटी (another name of arjuna) after doing great deeds and actions came back and had this child.
शतानीकस्य राजर्षेः कौरव्यस्य महात्मनः।
चक्रे पुत्रं सनामानं नकुलः कीर्तिवर्धनम्।।
Satanika (शतानीक) was named after Royal Rishi of Kuru Lineage who name was also Satanika .
ततस्त्वजीजनत्कृष्णा नक्षत्रे वह्निदैवते।
सहदेवात्सुतं तस्माच्छ्रुतसेनेति तं विदुः।।
Shrutasena (श्रुतसेन) got his name because he was born in Krittika Nakshatra (कृतिका नक्षत्र) which belong to Agnidev (Agnidev has another name called Shrutasena)