554. Vāruṇaḥ वारुणः 

Vāruṇa means given by Varuṇa (previous nāma). According to Rig Veda, sage Vasiṣṭha was inspired by Varuṇa. In some verses of Rig Veda, he has been described as the son of Varuṇa. Sage Vyāsa is the great grandson of sage Vasiṣṭha. Sage Vyāsa is invoked in the first dhyāna verse of this Sahasranāma. 

555. Vṛkṣaḥ वृक्षः 

Vṛkṣa means tree. He stands tall and firm like a tree. His act of sustenance is subtly conveyed here. When a soul undergoes transmigrations (known as saṁsāra), it takes rest at some point of time, however subject to its karmic account. This rest is called sojourn in the higher cosmic planes. This rest for the soul is also subtly conveyed here. 

Śvetāśvatara Upaniṣad (III.9) compares Brahman to a tree. It says, “vṛkṣaḥ iva stabdhaḥ वृक्षः इव स्तब्धः” which means “(The Self stands alone in the glory of its being) fixed like a tree. 

Kṛṣṇa says in Bhagavad Gītā (XV.1), “He who knows the pīpala tree, which is said to be imperishable with its roots in the Primeval Being, whose stem is represented by Brahmā (god of creation and is different from Brahman) and whose leaves are Vedas, is a true knower of Vedas.” 

Kaṭha Upaniṣad (II.iii.1) cites the example of a tree in a different context. It conceptualizes an inverted tree, with its roots up and foliage down. Root is compared to the Brahman and foliage to the material world. From the root, the universe appears as the material world. Foliage withers and blossoms again and this is compared to the birth and death of beings. The root of the tree remains the same, irrespective of the constant modifications taking place in its foliage. 

Bhīṣma, being a great scholar could recollect all these sayings, even during his death bed. When the Lord Himself is physically present to liberate Bhīṣma, it is but natural that one recollects all the Glories of the Lord. 

556. Puṣkarākṣaḥ पुष्कराक्षः 

Repetitive nāma 40. 

Nāma 40 explained this as “lotus eyed”. This nāma explains in subtle way that He is placed in the heart chakra (anāhata cakra) as the Self, often referred as the soul in a being. Without soul, no being can ever exist. 

This nāma conveys that He looks from within, all the actions (referred subtly as Puṣkarākṣa) of a being merely remaining as a witness. 

557. Mahāmanaḥ महामनः 

Mahāmana means “great mind” which is the Divine Free Will or His Free Will. He creates, sustains and causes death to all the beings through his Great Mind or Free Will. Instead of directly referring this as Free Will, this nāma subtly conveys the Divine Free Will, through which Brahman carries out all His actions. He does not act directly, but through His power called Māyā. Generally free will means any decision taken without any external influence.   

558. Bhagavān भगवान् 

This is derived from the word “bhaga” which means the one who has these six qualities viz. dignity, majesty, distinction, excellence, beauty and loveliness. All these qualities in eternal purity make Him as Bhagavān. When these qualities are tainted, he becomes a self or a being.

Though the whole universe is His manifestation, there is a significant difference in Him as the subject and the world as the object. When He manifests as the world or the object, all His qualities lose their original purity and become blemished. While pursuing spiritual path, an aspirant attempts to remove these blemishes and tries to realize his Original Nature (the Self). Self loses its original nature because of Māyā, the feminine dynamic energy, without which the existence of the universe is not possible.
Feminine gender of Bhagavān is Bhagavatī. Bhagavān and Bhagavatī are said to be the Father and Mother of the universe.

559. Bhagahāḥ भगहाः

This is derived from the word Bhagahan, which means the destroyer or Bhaga, discussed in the previous nāma. At the time of annihilation, He withdraws all the six qualities of Bhaga unto Himself. When He is pervading the universe, all these qualities exist in the universe in a distorted manner. Annihilation is a process exactly opposite to creation. At the time of first creation, there existed nothing and at the end of annihilation, there will be nothing left in the universe. Universe (multiple galaxies) will go back to the pre-creative period. As no traces will be left after annihilation, He dissolves unto Himself, all that exist with no traces left anywhere. Only out of compassion to the beings, He recreates the universe and the process of evolution begins all over again. 

This nāma also conveys that the universe is being maintained by the six qualities of bhaga discussed in the previous nāma. 

560. Ānandī आनन्दी 

He is in the form of eternal Bliss. Brahman is the congelation of sat, cit and ānanda (existence or truth, consciousness and bliss). He is revered as Bliss, as He is always in the state of eternal happiness. He is always in the state of Bliss because He is both Bhagavān and Bhagahā. 

When free will is not operation, human mind oscillates according to the inputs received from the material world. When the mind is disconnected from the external world, his free will becomes operative making the mind immune to external influences. When the mind becomes one with the Self (known as Self-realization), who is merely witnessing all our actions, state of the aspirant’s mind also is pervaded by His Bliss.

561. Vanamālī वनमाली

In nāma 216, it has been discussed that the garland He wears is known as Vaijayanti. This garland is also called vanamāli, meaning forest flowers. Vaijayanti not only means five tanmātra-s, but also means the five basic elements. Planet earth was finally created out of these five principal elements - sky, air, fire, water and finally the earth. Earth is grossest of all His creations.

This nāma adores Him as Vanamālī, as He constantly wears the most celebrated garland Vaijayanti.

562. Halāyudhaḥ हलायुधः

Halāyudha means plough weaponed. Lord Viṣṇu incarnated in the form of Balarāma. This is explained in Nārāyaṇīyam  canto 36.

Further reading on Balarāma:

His nineteenth incarnation is Balarāma.  He is the elder brother of Lord Kṛṣṇa.  It is generally accepted that Śeṣa, the well known snake on which Nārāyaṇa lies down (ananta sayana) is incarnated as Balarāma.  He is considered as an embodiment of wisdom and knowledge. Balarāma is also known as Sankarshana.  It is also said that both Balarāma and Kṛṣṇa are of same identity with different bodily forms.  At the time of Balarāma’s death, it is said that a huge snake went out his body through his mouth. When Baladeva (another name for Balarāma) appeared as the seventh child in the womb of Devaki, she could understand that this was a divine child. Even Kamsa could sense His potency and was scared, thinking he may have been tricked by the prophecy that he will be killed only by the eighth child of Devaki. At this time Kṛṣṇa instructed Yogamāya, His internal potency, to transfer the unborn child from the womb of Devaki to that of Rohini, another wife of Vasudeva, who was hiding from Kamsa in the house of Nanda Maharaja in Gokula.  This is how Balarāma escaped death from the hands of Kamsa.  Balarāma and Kṛṣṇa co-existed at the same time.  There are other versions as well