In פתיחת אליהו it mentions the עתיקא קדישא, which literally means the Ancient Holy One. Is that a name of HaShem or referring to something else?
This is discussed in Sefer Eitz Chaim, Heichal Shlishi (Heichal HaKeterim), Sha'ar Rishon (Sha'arei Atik).
Atikah Kadisha together with Arich Anpin is the highest level of existence in terms of the hishtalshelut of the universe. (They correspond to the individual aspects of maleness and femaleness and their union to be truly one.) As the Ari z"l explains, they are both included in Keter of Atzilut. It is not a name of HaShem, but above the level of names.
At this level of creation, the language of the Torah as transmitted by the Ari z"l is talking about paradigms for existence (what is called Shechinah in other places), meaning how we relate to or perceive G-d. In the language of Chassidut, this is usually delineated as the distinction between Atzmut, the framework of existence (In terms of allegory, think like the bones of the skeleton are the framework upon which the body is built. This is what we relate to.), and Mahut, G-d as He truly is (which is beyond the ability of all created beings to perceive at all).
This concept of Atzmut has an external aspect and an internal aspect just like our bones have an external, hard, white covering and an inner, soft, red marrow, which is the distinction between Arich Anpin and Atikah Kadisha.
Another important concept to understand about עתיקא קדישא is that it is from the root עתק which has a connotation of copying or translating.
In other words, עתיקא קדישא is introducing the paradigm of Safrut (Scribal Arts) and the Faithful Sofer (the Holy Scribe). In this usage, Holy has the connotation of copying without error. Whatever is being copied is a faithful copy of the original. But at the same time, it is a translation from the original into our native language. This corresponds to the many laws associated with the copying of a Sefer Torah (that it must be a perfect copy down to the letter or it is invalid) and also to the idea mentioned in Noam Elimelech and many other places, that:
וזהו ידוע דאורייתא וקב"ה כולא חד
That G-d and the Torah are one.
And this idea, that creation is a reliable translation of G-d's oneness is in keeping with the text many recite on Erev Shabbat known as Patach Eliyahu (Eliyahu the Prophet opened and said...) which describes the entire concept of the sephirot and states:
אַנְתְּ הוּא חַכִּים וְלָא בְּחָכְמָה יְדִיעָא. אַנְתְּ הוּא מֵבִין וְלָא בְּבִינָה יְדִיעָא. לֵית לָךְ אֲתַר יְדִיעָא. אֶלָּא לְאִשְׁתְּמוֹדְעָא תּוּקְפָךְ וְחֵילָךְ לִבְנֵי נָשָׁא וּלְאַחֲזָאָה לוֹן אֵיךְ מִתְנַהֵג עָלְמָא בְּדִינָא וּבְרַחֲמֵי. דְּאִית צֶדֶק וּמִשְׁפָּט כְּפוּם עוֹבְדֵיהוֹן דִּבְנֵי נָשָׁא. דִּין אִיהוּ גְבוּרָא. מִשְׁפָּט עַמּוּדָא דְאֶמְצָעִיתָא. צֶדֶק מַלְכוּתָא קַדִּישָׁא, מֹאזְנֵי צֶדֶק תְּרֵין סַמְכֵי קְשׁוֹט, הִין צֶדֶק אוֹת בְּרִית קוֹדֶשׁ, כּוֹלָא לְאַחֲזָאָה אֵיךְ מִתְנַהֵג עָלְמָא, אֲבָל לַאו דְּאִית לָךְ צֶדֶק יְדִיעָא דְאִיהוּ דִין, וְלָא מִשְׁפָּט יְדִיעָא דְאִיהוּ רַחֲמֵי, וְלָא מִכָּל אִלֵּין מִדּוֹת כְּלָל:
That You, G-d, are wise but not with a known wisdom, etc.
That it uses different forms of the words for wisdom and understanding, etc. than are used for us, His creations. We, His creations, are, so to speak, a reliable copy of Him, who is truly one.