May 29th is the date for the official U.S. rescission of its designation of Cuba as a “State Sponsor of Terrorism.” This was covered in a prior post.
In anticipation of that rescission, Cuba’s President, Raúl Castro on May 12th said to journalists, “This sort of unjust accusation [sponsor of terrorism] is about to be lifted, and we’ll be able to name ambassadors.” 
Later that same day the U.S. State Department said, “an exchange of ambassadors would be a logical step . . . only once we re-establish diplomatic relations. We do not have a fixed time for that. We are still in negotiations . . . with Cuban authorities about re-establishing diplomatic relations.”
The latter statement confirms there are still unresolved issues for such normalization.
The main one appears to be whether or not U.S. diplomats in Cuba would be free to travel wherever and whenever they wanted and Cuba’s complaints that U.S. diplomats having meetings with Cuban dissidents amounted to meddling in Cuba’s internal affairs in violation of international treaties on diplomatic relations.
Indeed, yesterday President Castro stated he had told President Obama that such diplomatic encounters remained Cuba’s chief concern about establishing normal relations, particularly programs at the American Interests Section in Havana to assist independent journalists. In Castro’s own words (English translation), “I told . . . President Obama . . . that . . . I was most worried about . . . they continue to do illegal things. For example, graduating independent journalists. [The U.S. gives Cuban journalists] . . . I don’t know how many classes, on screen, in teleconferences from the United States. I don’t know if they give them a diploma and of course they give them their corresponding monthly payment.”
The U.S. Interests Section does offer free classes in journalism, English and information technology, but students are not paid by the U.S.
Another unresolved issue for establishment of normal diplomatic relations is the U.S. insistence that it must be allowed to bring secure shipping containers into the country, in accordance with global diplomatic protocols.
Castro in his remarks to journalists yesterday also mentioned that the U.S. embargo or blockade “must be removed”  and the Guantanamo Naval Base, which was leased after the U.S. had taken over Cuba in the early 20th century, “should be returned to Cuba.”  Neither of these will happen immediately, and the latter may never happen.
Cuban negotiators are due to arrive in Washington as soon as this week for a fourth round of talks. Presumably at least some of these issues will be at the top of the agenda.
Once the U.S. and Cuba resolve these issues, each country first would change the names on their respective buildings from “interests section” to “embassy.” And the U.S. presumably would change the title of Jeffrey DeLaurentis, the current “Head of Mission” of the U.S. Interests Section in Havana to “Charge d’Affaires” or “Acting Ambassador.” (He already has the title of “Ambassador” from the previous Senate confirmation of his appointment as Alternate Representative for Special Political Affairs at the U.S. Mission to the United Nations.)
President Obama at some point would appoint someone to be the U.S. Ambassador to Cuba, but under Article II, Section 2(2) of the U.S. Constitution, the U.S. Senate, by a simple majority vote, has to give its “advice and consent” to such an appointment. Such a vote would be taken after hearings and consideration of the appointment by the U.S. Senate Foreign Relations Committee, currently chaired by Senator Bob Corker (Rep., TN). Two members of the Committee, both Cuban-Americans, Marco Rubio (Rep., FL) and Bob Menendez (Dem., NJ), are ardent foes of U.S.-Cuba reconciliation and are potential problems for such confirmation. And Rubio is the Chair of the Subcommittee on Western Hemisphere, Transnational Crime, Civilian Security, Democracy, Human Rights, and Global Women’s Issues, which might consider the nomination before the full Committee does so.
 This post is based upon the following: Archibold, Cuba Ready to Exchange Diplomats, Raúl Castro Says, N.Y. Times (May 12, 2015); Trotta, Cuba’s Castro concerned over “illegal” activity at U.S. mission, Reuters (May 12, 2015); Assoc. Press, US and Cuba Ambassadors To Be Named Soon, N.Y. Times (May 12, 2015); Miroff, Cuba ready to name U.S. ambassador, Castro says, Wash. Post (May 12, 2015); Hernández, French President culminated successful visit to Cuba, Granma (May 21, 2015) (Google translation); Raúl: The process of updating the Cuban economic model “goes well, our pace” (+ video), Cubadebate (May 12, 2015) (Google translation); U.S. State Dep’t, Daily Press Briefing (May 12, 2015).
 Prior posts discussed bills to end the embargo in the U.S. House of Representatives and the U.S. Senate that were introduced in this Session of Congress. According to the Library of Congress, as of May 12th there had been no committee action on any of these bills.