Damodar (दामोदरः)
As mentioned by Adi Sankara in Vishnu Sahasranamam verse 53
1. दमादिसाधनेनोदारोत्कृष्टा मतिर्या तया गम्यत इति दामोदरः
one whose mind is transformed by yoga method of damah (दम: – control over senses), he called Damodar
2. यशोदया दाम्रोदरे बध्द इति वा दामोदरः
One who was tied by Yasodha using rope (दाम) at waist (उदर)
3. As mentioned in Vishnu Purana part 5, 6.21 and Brahma Purana 184.41
तोयर्मध्यगतं बद्धं दाम्ना गाढं तथोदरे।।
ततश्च दामोदरतां स ययौ दामबन्धनात्।
Lord Krishna was tightly tied using a rope (दाम ) from the waist (उदर), therefore being tied with a rope (दाम) he is called as Damodar (दामोदर)
