I can't believe I figured this out.. lol I am always so dependent on the help of others I felt the need to share my findings.
I also am using a web page to pull several tables and wanted the "table name" to be associated with the data automatically. I wanted this not to be manual so the connection will be automated and auto input the unique table identifier.
After you add all the tables you want from the URL if you highlight one at a time and select Advanced Editor it should show you a the source as a webpage and then a Data# = Source{#}[Data]. The Source # should be unique to each table it pulled in. That source # is referencing the table. Several minutes of tinkering led me to the following code for a custom column. "=Source{#}[Caption]". Adjust the # to whatever the source number shows on your table you are connected to on the URL.
I know this is from 2014 but I am still having this problem in 2019 and can't find a solution. This worked for me. Hopefully it is a good fix.