Yes.
The land was granted the Island type, and Islandwalk checks the type of the card (not its name).
702.14c A creature with landwalk can’t be blocked as long as the defending player controls at least one land with the specified subtype (as in “islandwalk”), with the specified supertype (as in “legendary landwalk”), without the specified supertype (as in “nonbasic landwalk”), or with both the specified supertype and the specified subtype (as in “snow swampwalk”). (See rule 509, “Declare Blockers Step.”)
Incidentally, that also means you can tap it for blue mana.
305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words “basic land type,” it’s referring to one of these subtypes. A land with a basic land type has the intrinsic ability “{T}: Add [mana symbol] to your mana pool,” even if the text box doesn’t actually contain that text or the object has no text box. For Plains, [mana symbol] is {W}; for Islands, {U}; for Swamps, {B}; for Mountains, {R}; and for Forests, {G}. See rule 107.4a. See also rule 605, “Mana Abilities.”