The appearance of Lord Kṛṣṇa at the deathbed of Bhīṣmajī is due to his being an unflinching devotee of the Lord. Arjuna had some bodily relation with Kṛṣṇa because the Lord happened to be his maternal cousin. But Bhīṣma had no such bodily relation. Therefore the cause of attraction was due to the intimate relation of the soul. Yet because the relation of the body is very pleasing and natural, the Lord is more pleased when He is addressed as the son of Mahārāja Nanda, the son of Yaśodā, the lover of Rādhārāṇī. This affinity by bodily relation with the Lord is another feature of reciprocating loving service with the Lord.
Bhīṣmadeva is conscious of this sweetness of transcendental humor, and therefore he likes to address the Lord as Vijaya-sakhe, Pārtha-sakhe, etc., exactly like Nanda-nandana or Yaśodā-nandana. The best way to establish our relation in transcendental sweetness is to approach Him through His recognized devotees. One should not try to establish the relation directly; there must be a medium which is transparent and competent to lead us to the right path. SB 1.9.22
Bhīṣmadeva is conscious of this sweetness of transcendental humor, and therefore he likes to address the Lord as Vijaya-sakhe, Pārtha-sakhe, etc., exactly like Nanda-nandana or Yaśodā-nandana. The best way to establish our relation in transcendental sweetness is to approach Him through His recognized devotees. One should not try to establish the relation directly; there must be a medium which is transparent and competent to lead us to the right path. SB 1.9.22