Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever cheats us is not one of us. [Reported by Imam Muslim]. The Hadith is among the comprehensive words of the Prophet (Salla Allahu Alaihi Wa Sallam). It establishes a basic rule that is to be considered while dealing with people. The practice you are asking about is a kind of cheating regardless of origin of the company whether it belongs to Muslims or not. Therefore, try to advise the owners of the company not to use the commercial trademark of the other companies. If they accept your advice then you may work with them; otherwise leave them. Know that Allah will grant you better than what you have left for His Sake. Allah Says (interpretation of meaning): {…And whosoever fears Allah and keeps his duty to Him, He will make a way for him And He will provide him from (sources) he never could imagine. And whosoever puts his trust in Allah, then He will suffice him….}[65:2-3].
Allah knows best.