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)

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