It depends on whether you're using DAO or ADO. With DAO, use the dbFailOnError option and the call will generate a run-time error if, for example, the query can't execute because it would cause a key violation.
With ADO, the call will generate a runtime error if not successful, also you can check the 'RecordsAffected' parameter which is the 2nd parameter for the Execute method.
'DAO style:
Dim db As DAO.Database
'(set db by opening a database)
db.Execute "UPDATE TABLE1 SET NAME='AAA'", dbFailOnError
'OR -- ADO style:
Dim cn As ADODB.Connection
Dim lngRecs As Long
'(set cn by opening a database)
cn.Execute "UPDATE TABLE1 SET NAME='AAA'", lngRecs, adCmdText