I'd suggest:
Al-Mamlakah al-‘Arabiyyah as-Sa‘ūdiyyah
or:
Al-Mamlakah al-‘Arabiyyah as-Su‘ūdiyyah

Eldad:
Thank you, I have added your second suggestion with the hyphenized "as-Sa'udiyyah".

Alexander:
I still have to add a few more countries with their names in local languages. I do this in order to give the names of countries and languages in the Amazigh language (tafṛensist, tapuṛtugalit, tamaziɣt, taɛṛabt, talmanit, tarusit, tirlandit, taswidit, taɛebrit, tahendit, etc.).

Later, I will write much more examples about every country in the world.

By the way, this "hybrid looking mix" you are talking about is an interesting phenomenon in translation, and I try to explore it too ^^

Amastan:
I believe you should capitalize only the first "Al-"; the others usually remain lowercase, as well as the "as-", which is also written in lowercase.

And, if you wrote "Al-‘Arabiyyah", why not write "Al-Mamlakah*"?
Otherwise:
"Al-‘Arabiyya" and "Al-Mamlaka".

Eldad:
Thank you for your tips to standardize the transcription of this name.

For the lowercase, do you mean that I should write "Al-mamlakah"? I think it's better to capitalize every first letter of every word in that transcription.

Fine. Then, if you opted for uppercase, I guess you should stick to it also with the last "Al-", which turned into "As-" due to the adjacent "S":
As-Sa‘ūdiyyah

I knew you would say this ^^ OK amiko ^^

You read my mind, then ^v^

By the way, this "hybrid looking mix" you are talking about is an interesting phenomenon in translation, and I try to explore it too.

Oh, if this happens for the sake of science I will be silent. ☺

Eldad:
Maybe when you translate too much, you will develop new capabilities ... gifts that haven't been explained by modern science yet ^^

Alexander:
Well, there is a bit of science in it - hehehe ... First, I would like to use the names of languages in Amazigh as often as possible in the Tatoeba corpus. Secondly, I would like to push translation to its limits through some patterns like this one of mixing two languages in the same sentence ^^

Hayastan:

Gracias por tu pregunta. En verdad, la frase inglesa, asi' como la del amazigh (bereber), muestran como se dice el nombre de la Arabia Saudita en arabe. Pero pienso que lo que propones es también interesante - en este caso, tu traduccio'n española indicari'a la manera (y no la forma) en la que la Arabia Saudita se llama en arabe.