Anglicize is often capitalized in the U.S., and sometimes in other countries.
From the en.wikipedia.org
Historically, Jews in Hollywood were encouraged to anglicize their names to avoid possible discrimination.
From the en.wikipedia.org
I guess that was how he himself chose to anglicize it.
From the en.wikipedia.org
Later on he would anglicize his name to David Seymour.
From the lightbox.time.com
More examples
Anglicise: make English in appearance; "She anglicised her name after moving from Paris to London"
Anglicisation or anglicization (see -ise vs -ize) is a process of conversion of verbal or written elements of any other language into a more comprehensible English form for an English speaker, or to become English in form or character.