You can specify the Finder or System Events to expand the name and remove this part from the full name. This will also avoid problems with names with periods in them or extensions that may not be what you think.
set someItem to (choose file) tell application "System Events" to tell disk item (someItem as text) to set {theName, theExtension} to {name, name extension} if theExtension is not "" then set theName to text 1 thru -((count theExtension) + 2) of theName
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