Gave wrong name and governed after false claims (9)

'gave wrong name' is the definition.
(called by the wrong name)

'governed after false claims' is the wordplay.
'governed' becomes 'led' (lead can mean to govern or rule).
'after' means one lot of letters go next to another.
'false' is an anagram indicator.
'claims' with letters rearranged gives 'miscal'.
'led' put after 'miscal' is 'MISCALLED'.

'and' is the link.