Q:

How do I add this to this string query?

How do I add the same select * from database2.western thing but with where name='" and merged with this code (in the same query)
string Query = "select * from database2.western where id='" + comboBox1.Text + "'  ;";

A:

You should never use user input directly in an SQL query - it leaves you open to an SQL injection attack.
If you did really want to, then use:
string Query = "select * from database2.western where id='" + comboBox1.Text + "' OR name = '" + comboBox1.Text+ "'  ;";

In practice you should, at the very least, escape any quote marks in the user input. However, it's likely that whatever SQL library you are using has some kind of escape method. Assuming it does, and it's called escape, you could use:
string idOrName = escape(comboBox1.Text);
string Query = "select * from database2.western where id='" +idOrName + "' OR name = '" + idOrName + "'  ;";

Or better, if your library supports parameterised queries, something like:
string Query = "select * from database2.western where id=? OR name = ?";
DatabaseEngine.runParameterisedQuery(Query, idOrName, idOrName);

This is pseudocode - replace DatabaseEngine.runParameterisedQuery with something that works for your library.

