What is the default Name of Byzantium game rule in CK3?

Byzantine Empire: The name of the Byzantine Empire will be unchanged. (patch 1.20.1.2)

Does changing the Name of Byzantium rule disable achievements?

No: none of its 7 settings carries the flag blocks_achievements in patch 1.20.1.2.

Game rule · Historicity

Name of Byzantium

Byzantine Empire · default
Eastern Roman Empire
Roman Empire
Empire of Romania
Empire of the Greeks
Basileia tōn Rhōmaiōn
Unholy Roman Empire

Name of Byzantium is a game rule in Crusader Kings III (Historicity) with 7 settings: Byzantine Empire (the default), Eastern Roman Empire, Roman Empire, Empire of Romania, Empire of the Greeks, Basileia tōn Rhōmaiōn and Unholy Roman Empire. None of its settings disables achievements. Patch 1.20.1.2, from game/common/game_rules/00_game_rules.txt.

This section as JSON: /raw/game-rules.json

Quick answers (2)

What is the default Name of Byzantium game rule in CK3?: Byzantine Empire: The name of the Byzantine Empire will be unchanged. (patch 1.20.1.2)
Does changing the Name of Byzantium rule disable achievements?: No: none of its 7 settings carries the flag blocks_achievements in patch 1.20.1.2.

7 settings

Byzantine Empire
Default
The name of the Byzantine Empire will be unchanged.
default_name_of_byzantium
Eastern Roman Empire
The name of the Byzantine Empire will be changed to the Eastern Roman Empire.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = eastern_rome_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
eastern_rome_name_of_byzantium
Roman Empire
The name of the Byzantine Empire will be changed to the Roman Empire.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = roman_empire_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
roman_empire_name_of_byzantium
Empire of Romania
The name of the Byzantine Empire will be changed to the Empire of Romania.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = romania_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
romania_name_of_byzantium
Empire of the Greeks
The name of the Byzantine Empire will be changed to the Empire of the Greeks.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = empire_of_the_greeks_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
empire_of_the_greeks_name_of_byzantium
Basileia tōn Rhōmaiōn
The name of the Byzantine Empire will be changed to the Basileia tōn Rhōmaiōn.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = rhomaion_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
rhomaion_name_of_byzantium
Unholy Roman Empire
The name of the Byzantine Empire will be changed to the Unholy Roman Empire.
The script checks it 2 times, in 2 places
On actions (the game's own hooks) 2
- on_game_start
- on_game_start_after_lobby
Every has_game_rule = unholy_roman_empire_name_of_byzantium in game/common and game/events, by the top-level object it sits in.
unholy_roman_empire_name_of_byzantium

Source: game/common/game_rules/00_game_rules.txt line 503 (key name_of_byzantium), modifiers from game/common/modifiers, names from the English localisation; Crusader Kings III 1.20.1.2.