This depends on what customs and practices we are talking about, as the heraldric and ideological traditions were almost universally tailored to meet the individual cultural contexts of the successor states. To narrow the playing field a bit I am going to focus on established tradition by the dynasty as represented by the royal family in their propaganda and capacity as rulers.

It is worth noting that there was no uniform adoption of Egyptian customs in the dynasty, but rather an adoption of certain customs and symbolism within certain contexts for specific political or religious benefits. So instead of a singular choice made by a member or members at the beginning of the dynasty it was a series of interlocking changes that continued to shape and reinvent the identity of the dynasty until well into the reign of its last monarch.

The popularity of the Isis and Serapis cult outside of Egypt as well as Egyptian iconography demonstrates that within the Hellenistic and Roman world these still held significance and relevance in the popular imagination. And although a popular image exists of the Ptolemaic dynasty wholly adopting the trappings of Pharaonic regalia, in actuality their court remained distinctly Hellenistic. Nearly all of the iconography used outside of Egypt by the Ptolemaic dynasty was designed to appeal to the wider Hellenistic audience, and given the extent to which Alexandria and the Greek poleis were Hellenized, this aspect would have been important within Egypt as well. The symbols depicting them like the double eagle and cornucopia, both symbols of Hellenistic power and magnanimity. The extensive solar symbolism employed by the Ptolemies was effective in an Egyptian context as it invoked imagery of Amun-Re and Horus but it also translated into universal ideas of divinity, regality and imperialism. While in Egypt they associated themselves with Pharaonic dynasties and were represented as Egyptian kings and deities, in their more Hellenized territories such as Cyprus, Cyrene and Coele-Syria they assumed the Greek title of Basileus or king and outside of temple inscriptions and other dedications within Egypt they were not referred to as Pharaohs. The association with Osiris and Isis within an Egyptian context became an association with Dionysius and Aphrodite both immensely popular in the Hellenistic Near East.

The Seleucid Empire was similarly not above invoking the royal and divine iconography of their conquered land and both integrated foreign deities into their dynastic heritage by displaying them on coinage, dedicating temples and sanctuary to their worship, and connecting them to their own mythological origins.

There is extensive evidence of the Seleucid dynasty making use of Mesopotamian and Semitic deities such as Marduk, El and Atargatis both in temple dedications and on coinage with images of syncretized deities such as El-Cronus or Zeus syncretized with various sky deities. The famous Antiochus Cylinder from the Temple of Ezida in Borsippa from the reign of Antiochus I and written in Akkadian exemplifies the connections the Seleucids drew between their dynasty and traditional Babylonian kingship:

Antiochus, the great king, the mighty/legitimate king, king of the world, king of Babylon, king of lands, king of Esagila and Ezida, first son of Seleucus, the king, the Macedonian, am I. When I decided to build Esagila and Ezida, the bricks for Esagila and Ezida I molded with my pure hands, (using) fine quality oil which I found in the land of Hatti, and for the laying of the foundations of Esagila and Ezida I brought (them).

In the month of Addaru on the 20th day, year 43, the foundation of Ezida, the true temple, house of Nabu, which is in Borsippa, did I lay. (O) Nabu, lofty son, wise one of the gods, the proud one, worthy of praise, most noble son of Marduk, offspring of Erua, the queen, who formed mankind, regard (me) joyfully and, at your lofty command which is unchanging, may the overthrow of the countries of my enemies, the achievement of my battle-wishes against my enemies, permanent victories, just kingshiip, a happy reign, years of joy, children in satiety, be (your) gift for the kingship of Antiochus and Seleucus, the king, his son, for ever.

Prince Nabu, son of Esagila, first born of Marduk, noble child of Erua, the queen, on your entry to Ezida, the true house, the house of your Anu-ship, the dwelling which pleases your heart, with rejoicing and jubilation, may - at your true command which cannot be denied - my days be long, my years many, my throne firm, my reign long lasting, under your lofty sceptre which sets the boundary between heaven and earth. May my good fortune be in your pure mouth, may I conquer the countries from sunrise to sunset, may I gather their tribute with my hands and bring (it) for the perfection of Esagila and Ezida.

(O) Nabu, first son, when you enter Ezida, the true house, may favour for Antiochus, king of lands, (and) favour for Seleucus, the king, his son, Stratonike, his consort, the queen, be in your mouth.

Most interesting and relevant to this question is the fact that the earliest known usage of distinctly foreign deities is the appearance of the Hellenized Egyptian deities minted in Phoenicia and Antioch during the Sixth Syrian War, specifically the Hellenized Isis, Zeus-Serapis and Harpocrates (a form of the Hellenized Horus). During this war, Antiochus IV intended to conquer Egypt, Cyprus and Cyrene, and in fact came very near, even being coronated as Pharaoh in Memphis before the Roman Republic forced him to abandon the campaign. These coins also display a left-facing version of the Ptolemaic eagle and could possibly have been to commemorate his victories over the Ptolemies or more likely, they were minted for use in the territories he planned to annex from the Ptolemaic kingdom. This second interpretation, combined with Antiochus' identification with the Pharaoh demonstrates that it was understood as being at least somewhat analogous to the already established use of foreign iconography in winning the hearts and minds of their subjects. It is mentionable that Alexander himself was named Pharaoh and made a precedent of showing respect for Egypt's traditions and this, along with the often positive outlook of Greek authors such as Herodotus on Egypt's peculiarities made an impression on the Ptolemids and their contemporaries.

During her marriage to Antiochus VII from 138-129 and during her co-regency with her son Antiochus VIII from 125-121, coins bearing the Egyptian goddess Isis on the reverse were minted in Antioch and Ptolemais Akko, further exemplifying the acceptance of Egyptian religious icons within a Seleucid context.

One important facet of the establishment of a perceived Hellenistic identity with and separate from the Egyptian was through the creation of an established heritage and continuity of Hellenic presence within Egypt. This is reflected in the mythological association of Alexander the Great as being a son of the Pharaoh Nectanebo and god Osiris (a story which bears similarities with Seleucus I's origin as being secretly a son of Apollo), to the Alexander Romance. Another good example of one of the forerunners of this trend was Callimachus, an Alexandrian scholar and poet at the Library of Alexandria under the patronage of Ptolemy II, among his numerous works are a series of poetic texts surviving only in fragments but which provide essential mythological and historical context for the Greek occupants of Alexandria by emphasizing a Hellenic legacy within Egypt and in particular Alexandria. He based his works on writings like the Odyssey, Argonautica, the Iliad and the Trials of Herakles (particularly the Nemean episode) although his poems are markedly brief unlike the epic format which he was said to revile. These fragments often provide origins and reasons behind contemporary rituals and traditions within Hellenistic Egypt and use other mythological traditions (such as the sequestering of Helen in Alexandria) to bring Egypt more fully into the realm of Greek mythological tradition whereas before it occupied a more liminal role. Other Hellenistic writers from the 3rd and 2nd centuries followed in this tradition as a means to legitimize and Hellenize the formerly foreign and in this way create a sense of permanence and propriety to Hellenistic Egypt. What this demonstrates is both a need for this legitimacy and a literary basis for it, owing to and in part driving, the academic growth in Alexandria and its emergence as capital of scholarship.

This manner of retroactively placing the new localities and dynasties within established mythologies and histories was frequent throughout the Hellenistic period and was an essential part of the formation and development of a Hellenic identity within and without the Helladic world.