This is the 17491st most frequent Turkish word.
i̇smini
"İsmini" means "his/her/its name" in English.
In this sentence, 'ismini' is used as the direct object (accusative case) to denote the name of a person that is being mentioned.
Onun ismini söyledim.
I said his/her name.
Here, 'ismini' refers to the name being the object of the verb 'söyledi' (told), again showing possessive and accusative usage.
Sana ismini kim söyledi?
Who told you their name?
In this usage, 'ismini' links to 'ağacın' (of the tree), with 'ismini' meaning 'its name' referring to the tree's name. It is still the direct object of 'hatırlayamıyorum' (I can't remember).