Is it considered forbidden to change one's Arabic name to a foreign name and lie about residing in a foreign country while working as a saleswoman for a foreign company?

It is permissible to change a name to achieve a benefit, as long as the new name does not contain a Shariah prohibition. Lying is forbidden, and if one needs to, they should use ma'areedh (euphemisms or ambiguous statements). Residing and working in lands of kufr (disbelief) necessitates adherence to the rulings of Shariah. If doing so leads to non-adherence to the religion, then it is obligatory for the Muslim to leave that situation, and Allah will compensate them with something better, for the Hadith (definition): "Indeed, you will not abandon anything for the sake of Allah, the Mighty and Majestic, except that Allah will replace it with something better for you than it."