Str = "select p.Patient_First_Name, p.Patient_Last_Name, h.Hospital_Name from patient p LEFT JOIN hospital h ON p.Hospital_ID = h.Hospital_ID "
+" where CONCAT(p.Patient_First_Name, CONCAT(' ', p.Patient_Last_Name)) LIKE '%" + p.getPatient().getPatientName().trim() + "%'";
Who knows? Your query looks like a simple join, so a sub-query shouldn't be necessary, but it depends what you want your query to do, doesn't it? However, it does need a PreparedStatement, as it's not a good idea to build your query with concatenated string parameters like this (Google "SQL injection").
Here's a general way to make sure your SQL is correct before you get it all tangled up in your Java code:
Take your SQL and run it in your database's SQL shell e.g. SQL*Plus if you're on Oracle.
Does it give you the results you expect?
If it does then you know your SQL is correct, so now you can put your SQL into your Java code.
If it doesn't give you the right results, fix the SQL and run it again in your SQL shell. Do this until you get the right results, then put your SQL in your Java code.
Also, pick a coding convention and stick to it e.g. upper-case for all SQL keywords.