Password is a reserved word in MySql. If you want to use a field with that name then everytime you use it in your code you should remember to put it between backticks:
`password` = ...
Said that your code has serious problems. You should never concatenate strings coming from the user input to form a sql text. This leads to syntax errors caused by parsing problem and to Sql Injection attacks. You shoul use a parameterized query like this
strSQL = "SELECT name FROM employer WHERE (login=@login AND `password`=@pwd"
Dim cmd As MySqlCommand = New MySqlCommand(strSQL, con)
cmd.Parameters.Add("@login", MySqlDbType.VarChar).Value = strUser
cmd.Parameters.Add("@pwd",MySqlDbType.VarChar).Value = strPaswoord
con.Open()
If cmd.ExecuteScalar() = Nothing Then
....
Finally you should also change the way you get your data because you want to minimize the trips to access the database for performance reason. You should SELECT both the Name and the EMail with a single query and use an MySqlDataReader to get the data.
Other problems present in your code are the lack of appropriate using statement around the connection and the security problem caused by a possible clear text password stored in the database.
Resolveoption?