أَنْ تَكُونَ عَلَمًا فِي الْعُجْمَةِ
Translation: It must be a proper name in the foreign language.
The phrase فِي الْعُجْمَةِ is important: the book is not merely asking whether Arabic speakers use a borrowed word as a name, but whether its proper-name status comes from the foreign language.
Ibrāhīm is the positive case; lijām shows why a foreign common noun does not meet this condition.