More names for you.

Asturian male names

Teodomir
Casio/ Casius
Lope
Adanino
Odoario
Gatón
Sarracino
Fortis
Lucas (Luke)
Gomez
Beato/ Beatus
Eterio/ Heterius

Asturian female names

Nuña/ Nunia


Hispanic Mark male names

Bera
Rampón
Alerán
Angelino
Sabarino
Viliesindo/ Wilesind

Hispanic Mark female names

Petronila


Let´s go with Al-Andalus names

Emires and Caliphes of Al-Andalus

Tarik (berber)
Muza ben Nusair
Abd-Al-Aziz ben Muza
Ayub ben Habib
Al-Horr
Al-Sama ben Malik
Abd-ar-Rahmán
Ambaza
Odra ben Abdala
Yahya ben Salema
Hodaifa ben Al-Ahguas
Otman ben Abunisa
Al-Haitam ben Obaid
Abd al-Malik ben Katan
Okba
Balec ben Baxir
Taalaba ben Salama
Abultajar
Toaba ben Salama
Yusuf
Hixem
Al-Hakem
Muhammad
Al-Mondir
Abd-Allah
Suleiman

Other andalusian names

Zeyad
Omar ben Abdallah Al-Muradí
Munuza (berber)
Habib
Maisara Al-Hakir (berber)
Baleg ben Biser
Katan
Umaiya
Halid ben Hamed as-Zanati (berber)
Mohawiya
Bader
Alkama
Teman
Ibrahim ben Sagara
Asim Al-Uryan
Abusaid
Abusuluad
Xaquia
Husein ben Yahya
Omar
Malik
Hasdail ben Saprut (jewish)
Abul Hattar
Darrag Al-Kastali (berber)
Ubaid Allah ben Kasim
Chammas
Isa
Garbib
Amrus
Obaidala
Abu Hafs
Umar
Idris
Ziryab (persian)
Nasr
Hasim
Sadun
Ibn Marwan
Omar ben Hafsun
Aisun
Hafs
Sauwar
Said
Hagag
Haldun
Gad
Umaiya
Bakr
Aben Mastana
Ahmed
Chafar
Saih Al-Aslami
Halaf
Aben Marwan
Galib
Nachda ("slav", or european slave)
Abu Alí
Mushafi
Aben Gannun
Al-Mugira
Ibn Abu Amir Muhammad, named Al-Mansur Billah (Almanzor in spanish), or "the victorious". General, politic and dictator of Al-Andalus between 978 and 1002 AD). Many times victor over christians, and conqueror of Barcelona, Coimbra, Leon, Zamora and Compostela. He preffered sack and/or exterminate those cities more than conquer.
Chaudar
Bologgin
Askalacha
Ziri ben Atiya
Wadih
Al-Mudaffar
Zawi
Hairan
Muchahid
Gawhar
Ibn Rumatris


Andalusian female names

Tarub
Subh
Asmah
Radia
Fatima
Lobna
Fadal
Calam
Adal

About traits: I think all the usual christian traits are valids for asturian generals. Could be posible, if you are going to adopt the BI "religious-type", add a new trait: adopcionist believs. Adopcionist was a teological controversy in Spain in VIII century, and separated Asturian Church from mossarab (goth cristian in andalus kingdom) church, bringing it near roman european church. Adoptionist believs in a asturian general must (as donatist or arian believs in a roman general in BI) decrease popularity and public order if that general is a governor.

I think important trait for a christian general (Asturian, Navarre, Catalonian) is despise or hate muslims. Of course the same about christians for an andalusi general. Don´t forget war in Spain had an central motivation about religion.

I don´t know if you are going to reintroduce offices, as in MTW and BI, but if you are interested, here are some of them:

Andalusian offices (or ancillaries):
Sultan, at 929 Caliph: king or faction leader
Haxib: Prime minister or Chancellor of Palace. head of Royal House, Chancillery and Public Treasure
Vizir: Each one of minister or state secretaries.
Amir or wali: governor of a province. Before Caliphate first emir were the effective gobernor of all Andalus.
Cadi: judge or major of a town. Cadi aljamaa: head of all judges of the caliphate.
Sahib Surta or Chorta: head of policy of Cordoba.
Sahib as Sikka: head of the coin factory

Some ancillaries: Mursif or tax collector (+ in tax collection and in administration), Akim or auxiliar judge (+ law and public order), Al-wazir or policy agent (+ in public order), Mutashib or inspector of weights and measures (+ in trade, farmer production, tax and population grow), Caid or general (+ in personal security and command), ulema or alim, a muslim saviour (+ in muslim conversion and happiness in muslim provinces, - ), faqui, teacher at university (+ in management and influence).

Real Ancillaries: Al-Gazal, a poet and ambassador; Aben Abd er Rabihi, enciclopedist and scholar; Aben Hani, poet; Azzobaidi, famous teacher of caliphas; Said of Bagdad, poet and epigramist; Habid, bard; Walada, princess and poet; Aben Zeidun, poet; Aben Jaldun, singer; Ziriab, musician; Abd el Malik ben Habib, Law expert; Aben Masarra, philosopher; Aben Hazam, philosopher (don´t forget that a philosopher improves management but decreases popularity of a general due to be suspect of heresy); Ahmed Aben Nasar, mathematician; Moslema ben Alcasim, astronomist, astrologist and alquimist; Maslama, astronomist: Yahya ben Ishak, physician; Said ben Abderrahibi, physician; Albucasim, famous chirurgeon around dark ages world.

Enough for today. Next day I´ll try to find trais and ancillaries for Asturias, and, if possible, of kingdom of Navarre (basques) and County of Barcelona (catalonians)