Just like in Jambu Dvip, Jambu tree has been identified, which tree in modern day is the Shaka tree?
what is the shaka tree after which sakadvip has been named.
The saka tree after which sakadvipa has named is Sagvan Or Teak.
Saka (Scythian) is a Sanskrit word which means Sagwan or Teak(Tectona grandis), generally grown in monsoon region.
See the section Origin of Saka
The saka tree and Sakadvipa is mentioned in - Shreemad Bhagvat Purana Skanda 5- Chapter -20 -Verse -24
एवं पुरस्तात्क्षीरोदात्परित उपवेशितः शाकद्वीपो द्वात्रिंशल्लक्षयोजनायामः
समानेन च दधिमण्डोदेन परीतो यस्मिन् शाको नाम महीरुहः स्वक्षेत्रव्यप
देशको यस्य ह महासुरभिगन्धस्तं द्वीपमनुवासयति ॥ SB 5.20.24 ॥
evaḿ purastāt kṣīrodāt parita
upaveśitaḥ śākadvīpo dvātriḿśal-
lakṣa-yojanāyāmaḥ samānena ca dadhi-maṇḍodena parīto yasmin śāko nāma mahīruhaḥ sva-kṣetra-
vyapadeśako yasya ha mahā-surabhi-gandhas taḿ dvīpam anuvāsayati
Outside the Ocean of Milk is another island, Sakadvipa, which has a width of 3,200,000 yojanas [25,600,000 miles]. As Krauncadvipa is surrounded by its own ocean of milk, Sakadvipa is surrounded by an ocean of churned yogurt as broad as the island itself. In Sakadvipa there is a big saka tree, from which the island takes its name. This tree is very fragrant. Indeed, it lends its scent to the entire island.
The Vishnu Purana and the Mahabharata's derive the name Saka-dvipa from the 'Saka tree' the modern Sagavana. In India the word Sagavana, a corruption of Sanskrit Saka is used up to this day to denote the teak tree. According to the Matsya Purana however, there was a Saka mountain in the Saka-dvipa and hence the land takes its name after the name of the mountain.