I think you could go three ways with 'global'
Firstly, Old Testament names would cover most Middle Eastern cultures as well as Europe:
Abigail, Rachel, Rebekah, Esther, Naomi, Ruth, Rachel, Leah, Lydia, Deborah, Sara, Sarah, Sarai
Abraham, Adam, Daniel, Joshua, Jacob, Joseph, Micah, Ezra, Isaac, Nehemiah, Reuben, Noah, Elijah, Elisha, Asher, Benjamin, David, Samuel, Solomon
Secondly, French/Italian/Spanish/Russian style names that just seem exotic or elegant wherever you are:
Sylvie, Simone, Amelie, Geraldine, Genevieve, Gabriella, Aurelia, Anastasia, Antonia, Mila, Livia, Julianna, Gianna, Eloise, Elodie, Sandrine, Marianne, Elisaveta, Petrova, Elisa, Marina, Rocio, Alejandra
Antonio, Alonso, Claud, Paulo, Pablo, Diego, Angelo, Alessandro, Alejandro, Marco, Rocco
Thirdly, names which do have their origins in a middle eastern or certainly non western culture but which have become widely used here too:
Alba, Aaliyah, Amina, Amira, Amara, Lana, Farrah,
Amir, Ibrahim, Ahmed