Does God give the stranger a "better" name because He knows how much more the stranger has to give up to follow Him (Isaiah 56:3-7)?

An excellent example of what the stranger has to give up is given in the book of Ruth. Ruth left her family, her native land and customs—everything that was familiar to her—and went with her mother-in-law to an unknown land to live among people whom she must have suspected would hate her (after all, she was a Moabite woman), all to follow God.

"'Look,' said Naomi, 'your sister-in-law is going back to her people and her gods. Go back with her.' But Ruth replied, 'Don't urge me to leave you or to turn back from you. Where you go I will go, and where you stay I will stay. Your people will be my people and your God my God'" (Ruth 1:15-16, NIV).

I know everyone focuses on the words, "Where you go I will go," but what about the words, "Your people will be my people and your God my God"? We can see in verse 15 that the other sister-in-law had gone back to "her gods." But Ruth made, at some time, the decision to become a follower of the God of Israel.

Ruth put her faith in God, made her decision to turn her back on the land of Moab and followed a whole new path, wherever that would lead her, despite the hardships or tragedies and despite Naomi's bitterness of the moment.

God valued Ruth's decision and faith, so much so that Ruth, a Moabite woman, married Boaz and was counted in the direct lineage of Jesus Christ.