There is currently a push by Deaf Hawaiians (ethnically Hawaiian or hapa -mixed- Hawaiian)[1] to return to the name Hawai‘i Pidgin Sign Language for their old sign language, not the newer name, Hawai‘i Sign Language (HSL). Some Pidgin signs are still in use and are based on Hawaiian words that Deaf Hawaiians embrace. They reject the newer name and version that they associate with outsiders.
The name Pidgin Sign Language has been used a long time, by Ethnologue as well as others. A 1915 Honolulu news article referred to Pidgin Sign Language being used in court to question a deaf witness.[2] The free online dictionary and translator website sensagent lists it as Hawai‘i Pidgin Sign Language.[3] This name is preferred by Deaf Hawaiians.
[1] Prominent Deaf Hawaiian spokespersons include Maile Paongo, Hilda Silva Lopez, and Joy Enos. They have a number of local supporters of all ethnicities who are Deaf, most of whom attended the Hawai‘i School for the Deaf and Blind.
[2] Deaf Mute Oath Taken for First time in Hawaii. The Hawaiian gazette. January 08, 1915, Page 4. https://chroniclingamerica.loc.gov/lccn/sn83025121/1915-01-08/ed-1/seq-4...
[3] http://dictionary.sensagent.com/Hawaii%20Pidgin%20Sign%20Language/en-en/...