First of all, "national parks" are an unconstitutional federal land-grab from the states, regardless of how benign or benevolent such act may seem at the time. The only valid federal ownership of state land is described in Article I, Section 8, Clause 17 of the U.S. Constitution which says:
[Congress shall have Power ] to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;--
National parks were not purchased upon consent by state legislatures for the use of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings, so national parks are unconstitutional federal acts. The states can make state parks according to the consent of the people and legislature of that state.
Secondly, because national parks constitute unconstitutional federal commandeering of state land, the state may reject and nullify such an act. Unconstitutional federal acts are by definition acts of tyranny - its just that some acts of federal tyranny begin with a happy face. Sates have the right and the duty to stand against such acts.
Here, Alaska can declare, on sound constitutional principle, that Denali was not purchased upon consent by the Alaskan state legislature for the use of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings and can, therefore, take back this land. If Alaska actually paid money to the feds for this land originally (I doubt it) then Alaska can pay back the equivalent or reasonable amount now. Most likely, the feds didnt pay for Denali in which case Alaska can simply assume control of the land upon notification to the feds (NOT permission from the feds).
Laying that groundwork would make the next step of throwing out Obamas act of renaming Mt. McKinley an easy one. Most likely Alaska would simply make this a state park. Either way, it is ALASKA, NOT Obama, who can name the mountain whatever it wants.
Other than getting shot, what did McKinley do to deserve a mountain being named after him?
Look! A squirrel!