I can get the names of all files in a folder by doing this:
tell application \"Finder\"
set myFiles to name of every file of somePath
end tell
For a single file I found the answer here, copied below.
set theFileName to "test.jpg"
set thePrefix to text 1 thru ((offset of "." in theFileName) - 1) of theFileName
Based on Lauri Ranta's nice solution, which works for extensions that Finder doesn't know about:
set delims to AppleScript's text item delimiters
set AppleScript's text item delimiters to "."
set myNames to {}
tell application "Finder"
set myFiles to name of every file of (path to Desktop)
repeat with myfile in myFiles
set myname to name of file myfile
if myname contains "." then set myname to (text items 1 thru -2 of myname) as text
set end of myNames to myname
end repeat
end tell
set AppleScript's text item delimiters to delims
return myNames