I am new to Websphere, and at this client site, we are running an older version of Websphere in an older version of RAD. I used a python script to define a queue factory and some queues, using a script provided by another individual at the site. However, there was not mention of a queue manager in the script. It appears that the queues are created, I can see that they are defined in the Admin Console. Same is true for the queue factory. The admin console does not seem to expose the name of a queue manager, however.
I have been googling for a few days trying several different angles, but always come back to no answer. There seems to be tool called MQ Explorer, but that comes with Websphere MQ, which is not installed. No one here seems to have tried anything like this before, of if they have, may not have attempted what it is I am trying to achieve.
Ideally, what I would like to do would be to connect to the queue with a third party tool called MQ Visual Edit, for example.
There are about 3 or 4 questions here. Let's see if I can address all of them.
First, creating administered objects is completely separate from defining queues in the queue manager. Typically, the WebSphere MQ admin defines the queues and topics, then provides the host, port, channel, QMgr and queue/topic names to the WAS admin who then generates the matching connection factory and queue or topic objects. Defining the WAS objects does not create the corresponding WMQ objects, nor does it even imply that they exist. From your description, it sounds as though they may not have been defined on the QMgr.
In fact, it is not even obvious from your description that you are using MQ as your transport. If WAS is configured to use it's own JMS implementation (System Integration Bus or SIBus for short) then the connection factories and other objects may point to SIBus instead of WMQ. If you created a QCF for WMQ then someone should have already provided the details you are requesting - QMgr name, host, port and channel name.
WMQ Explorer is available as a free, stand-alone download called SupportPac MS0T. In order to use it, or any of the other 3rd party desktop tools such as MQ Visual Edit or SupportPac MO72 you will need to know the QMgr name as well as host, port and channel name. In addition, if the WMQ admin has enabled any security, you will need to be authorized to connect and, at a minimum, inquire on WMQ objects. The WMQ admin will provide these details to you. Assuming you have the QMgr details and are sufficiently authorized, just download and install SupportPac MS0T and point it at WMQ. Instructions on all things WMQ (including WMQ Explorer) are at the Infocenter pages. Since the stand-alone WMQ Explorer is V7 you will want the V7 Infocenter for any Explorer help. If the QMgr is at V6 then you may need to refer to the V6 Infocenter as well.
That answers the questions in the body of your post. The answer to the question in the title - how do I find out the QMgr name - is "ask the WMQ administrator." You should be given the name when you get the host, port and channel. That said, you often do not need it. A WMQ client will connect to any QMgr if provided the host, port and channel. This is what allows your client app to fail over to a different QMgr. Things like WMQ Explorer are the exception because they should not fail over. If you have a primary and backup QMgr, you typically want WMQ Explorer to see them both at the same time (so for example that you can configure them identically) and if one QMgr is down you want Explorer to report it as such. Therefore Explorer requires a QMgr name but most apps do not.