This is answered by Naryana Maharaja himself in the book “Walking with a saint” on page 4 which contains transcripts of morning walks and conversations he had with people in 2008.
Narayana Maharaja: Some ISCKON devotees preach that “Narayana Maharaja gives harinama and diksa initiation to the disciples of Srila Bhaktivedanta Svami Maharaja, and that is why he changed the name of Jadurani to Syamarani.”
Brajanath dasa: They call this re-initiation.
Narayana Maharaja: I never do this. Out of affection, I gave her this name. I cannot address her as Jadurani. I can address her as Syamarani. Srila Bhaktivedanta Svami Maharaja inspired me to give her this nickname. When she first came to him, he wanted her to understand Krishna’s Goodhood. He therefore gave her the name Jadurani, which is in relation to Krishna in Dvaraka. Now he wants her to further her understanding of Krishna in Vrndavana, so he inspired me to give her the name Syamarani.
So the name Syamarani is a nickname. Syamarani had already received diksa from a pure devotee, Srila A.C. Bhaktivedanta Swami (whith the emphasis on pure). There is no need to be re-initated then, to do so would be breaking vaishnava etiquette. Narayana Maharaja became a siksa guru to Syamarani, she received instructions and further deepening of her sadhana by associating with Narayana Maharaja.