To anglicize something is to change it so that it appears to be more English. Immigrants to the United States sometimes anglicize their names so they're more familiar to English-speaking Americans.
If you anglicize your house, you might decorate it in the style of a British tea room, and if you anglicize your Polish name, you make it sound less Polish and more English. Throughout history, places that were colonized by England were forced to anglicize many of their place names — one example is Kolkata, India, which was anglicized to "Calcutta" and changed back in 2001. Anglicize comes from the Latin root Angli, or "the English."