Who is the current Head of the Royal House of Hawai'i??
In short, there is no current Head of the Royal House of Hawai'i. The Ali'i Moi (King or Queen) would need to be elected by a council of high Ali'i (Nobles) from appropriate Ali'i Nui (Princes) & Heads of Legitimate Ali'i families.
Historically, under the Kingdom's constitution(s), if the king did not appoint a successor, a new king would be elected by the eligible Hawaiian Royals still alive. And in the history of the Hawaiian Kingdom, two Kings were elected when a successor was not appointed by the previous monarch i.e., King Lunalilo and King Kalakaua.
Presently there are two prominent Ali'i families with three candidates for consideration by the council of Ali'i when the occasion arises to elect an 'Ali'i Moi' - Head of the Royal House of Hawai'i.
They are the Lambert-Kawananakoa family headed by Prince Quentin; the Ellerbrock-Morris-Kawananakoa family headed by Princess Abigail and the Baker-Kamakahelei family headed by Prince Darrick.
In relation to both branches of the Kawananakoa family, their forebear Prince David Kawananakoa was indeed a named heir of the Kingdom of Hawai'i. However, it is stated in his last will and testament, in reference to his three children David Kalakaua, Abigail Kapiolani & Helen Lydia Lili'uokalani, that only David his son, would inherit his "orders, property and title." Yet David died without legitimate issue and left everything to his sister Helen Lydia Lili'oukalani.
None-the-less it is claimed that Helen Lydia Lili'uokalani's daughter Abigail Kinokiki Ellerbrock Kawananakoa was legally adopted by the Campbell family and thus she is no longer in the line of succession.
Secondly Abigail Kapiolani Lambert (Prince Quentin's Grandmother) was disinherited by her father Prince David Kawananakoa as stated 14 times in his will "...I therefore purposely omit the said KAPIOLANI from the provision of this, my last will and testament...' and gives KAPIOLANI to Abigail Campbell (her maternal grandmother) as her 'natural child'.
Therefore the 'Kawananakoa's' whilst high ranking Ali'i have no higher claim than any other Ali'i Nui of another family, and it could be argued less of a claim with their succession claim ending with Helen Lydia Lili'uokalani.
House of Kamakahelei
At this point in time no other Ali'i Nui other than Prince Darrick Lane Hoapili Liloa Kamakahelei Baker, Head of the House of Kamakahelei, Prince of Kaua'i who has a proven genealogical history with documented historical facts, have come forward to actively support the heritage and customs of the Hawaiian Kingdom.
There are a few low ranked Ali'i that are not direct descendants of the ruling Ali'i that occasionally make a claim to being Head of the Royal House of Hawai'i. As stated above, that position does not exist at this time. Only the Heads of the legitimate Royal Houses such as Prince Darrick as an Ali'i , who being the most senior members of the Royal family, are eligible to stand for election.
Most other claims are not and never have been eligible for election. At best they are Ali'i. Indeed any family that reportedly has a history of genealogical fabrication in order to cover up convicted criminals, treasonous and treacherous deceit against the Kingdom will never be considered as 'Royal' or taken seriously by Hawaiians. They are an insult to the nā kūpuna (ancestors), to the traditions of the 'O ke aupuni Hawai'i (Hawaiian Kingdom) and to the kānaka maoli (Hawaiian people).