When you did the search with 2 company names in the Criteria, everything worked ok, right?
When you do the second search, now looking for lastname, not company name, it still uses the Company name criteria?
Your Clear_Click event code looks ok to me.
Your BuildFilter code has this hard coded
so it's always looking for [company name]strSQL = "SELECT * FROM [Account List] " & _ "WHERE [Account List].[Company Name] IN(" & strCriteria & ");"