This is primarily an issue of path style. You're passing in a POSIX path whereas the Finder deals with either Mac-style paths (colon-delimited) or its own file class.
Despite it being many years, the Finder still can't automatically coerce between them, so you have to do it:
tell application "Finder"
set f to POSIX file "/Users/gmpro/Desktop/xxx.html"
set name of file f to (weekday of (current date)) as text
end tell
(note that I've added 'as text' to the target filename - that's because 'weekday' is actually an enumeration and will result in something like 'mon', 'tue', etc. whereas coercing it to text gives you the full day name ('Monday', 'Tuesday', etc.)