Śrī Śrī Guru Gaurāṅga jayate.
A very interesting occurrence. I love such incidents because it makes one think deeply.
Dreams as it were are manifestations of our external experiences, our deepest desires, even our anarthas. Many times dreams are as confusing as they are real. This I think you know.
Kindly don’t take offense to my opinion. First of all, as Śrīdhara Mahārāja once said, “It is possible that someone might be initiated by your Prabhupāda in a dream, but it is not very probable. Possible, but not probable.”
Śrīdhara Mahārāja further explained that if such an event actually occurred and Prabhupāda chose to initiate someone in a dream from among the 7 billion people of this planet, then we should expect to see something very wonderful from that chosen devotee – something very wonderful indeed. Not that after such an extraordinary event occurred, that the devotee will struggle in devotional service. Such a chosen devotee would be expected to rise very quickly as a spiritual leader, a giant of Kṛṣṇa conception and show us and give us something very exceptional, very wonderful. Such a devotee would not be ordinary in any way.
But don’t loose hope. I think your dream clearly shows that you are sincere and have a deep desire to be connected to a bona-fide guru in Kṛṣṇa consciousness.
There are numerous examples in Gauḍīya Vaiṣṇavism wherein dreams occurred with significant spiritual meaning. For example, in Caitanya-caritāmṛta, Ādi-līlā, Ch 5, verses 181 onwards is the narration that Kavirāja Gosvāmī received instruction in a dream from Lord Nityānanda to leave home and go to Vṛndāvana. Kavirāja Gosvāmī went to Vṛndāvana and there he met Raghunātha Dāsa Gosvāmī who then gave Kavirāja Gosvāmī mantra-dīkṣā. Kavirāja Gosvāmī is sometimes said to be a disciple of Lord Nityānanda because he received śikṣā from Nityānanda. He is also a disciple of Raghunātha Dāsa Gosvāmī because he received mantra-dīkṣā from him.
Bhaktivinoda Ṭhākura received instruction in a dream to take mantra-dīkṣā from Vipina Vihārī Gosvāmī. Bhaktivinoda received mantra-dīkṣā from the gosvāmī, but later accepted Jagannātha Dāsa Bābājī as his śikṣā–guru, as his bhāgavata-śikṣā-guru.
My opinion is that your seeing Prabhupāda in a dream and that he spoke to you shows your strong desire for Kṛṣṇa consciousness and to be connected to the line of Śrīla Prabhupāda by a bona-fide representative of Kṛṣṇa and Prabhupāda, but I do not think that the dream was your initiation in the formal sense, other than to encourage you to continue until you come in contact and surrender to sad–guru.
You mentioned the name ‘Śirva Nāga’, but I think you meant ‘Śiva Nāga’. In any case that is not a Vaiṣṇava name. Śiva Nāga is a name amongst certain Śaiva sects and Nāga-bābās, not amongst Vaiṣṇavas, at least not to my knowledge.
In all examples of bona-fide dreams it is seen that it is always necessary to receive initiation and proper śikṣā from a living Vaiṣṇava. Yes, unfortunately looking in present day ISKCON for a bona-fide guru connection is like looking in the darkness for a light. No amount of darkness produces light and no amount of ignorance produces Kṛṣṇa consciousness.
In my opinion, take your dream about Prabhupāda as encouragement, but not as initiation, not as dikṣā. Continue your search in all earnestness and pray to Lord Nityānanda to guide you.
Hope to have been some help to you.