In Mario Cassar, The surnames of the Maltese Islands: an etymological dictionary (2003):
(1) Greek — nickname (?); < Gk. Apapis
[De Soldanis], < apapy, a dandelion-like
weed; of uncertain application as a
surname. The surname Avap (a possible
cogante form) prevails in Italy.
(2) Arabic — nickname; tautological
form of Ar. ab meaning “father”
[Mikiel Anton Vassalli: Lexicon,
1796], in which case the aggregate term
term might suggest “grandfather,
ancestor” [MG]. The surname Ap
also prevails in Italy.
Old local forms: Hapap. (De)
The surname Apap features neither
in the Militia List of 1419/20
nor in the Angara Roster of the
1480’s, but figures prominently in
the Gozitan Crociata Records of
1533 [Wettinger:1980]. Probably, up
till then it was still confined to
Gozo; landowner Aloisio Apap is
recorded there in 1502 [De
Soldanis]. The Apap family erected
(or acquired) the beneficies of Ta
Caddiesa (1502), Habel Don Lorenzo
(1509), and Ta Ghammar (1576) [Montalto].
(1509), and Ta Ghammar (1576)
[Montalto]. The Apaps were one of
the prominent landed gentries of
Gozo who survived the Moorish
onslaught of 1551 [MG]. Don
Lorenzo De Apapis (1501-1586),
parish priest of St George's in Rabbato,
was actually taken into captivity, only
to be redeemed soon after the event
[Mifsud-Bonnici]; another priest,
Antonius Hapap, is recorded in Gozo in
1510 [Wettinger: 2002], In 1712 Filippo
Apap was created Marquis of Ġnien
is-Sultan by Grand Master De Rohan
- Several Jews bear the praenomen
Aba meaning “forefather, ancestor”;
Gk. papas also means “father”, a title
of respect used in addressing a parish
priest of the Orthodox Church.
EDIT: I've given this some thought overnight, and there are still some things from Cassar's entry that need clarification:
- What does the fact that there are two etymologies indicate? Are there two surnames Apap, one from Greek and one from Arabic? Or is there only one such surname, and the author doesn't know whether it comes from Greek or from Arabic?
- What exactly is this plant apapis, apapy? I've checked some Greek dictionaries and encyclopedias and found nothing. Given the connection between Malta and the Knights, it could be a dialectal Cypriot word.
- How did the "old local form" De Apapis form? Was it a Latinisation of Apap or a holdover from the Greek etymon?
- What are these surnames Avap and Ap that allegedly prevail in Italy? I haven't found any evidence of them.