Newbury/Newberry/Newbery means "new stronghold" (from Old English niwe, neowe, new, and buri, byri, fortified place).
In the United Kingdom, one town and a small number of villages have the name Newbury.
In the United States, the usual pronunciation of the name Newbury is as three distinct syllables, as if spelt New-Berry; with the exception of the region of New England where it is pronounced "Newbry".
However, in normal speech in the United Kingdom the name's pronunciation (both for places and people) is barely more than two syllables, either as if spelt Newbry or else with a slight uh sound after the -b-.
The same difference can be heard in the pronunciations of other names ending in -bury, such as Kingsbury, Hanbury, Salisbury, and Westbury.