Hey, thank you for your reply.
This is actually useful information because I was thinking along somewhat similar lines. I did not know about the small areas near a stream being called burnside, but I did read somewhere that a "burn" was a term used to refer to a stream.
To further clarify, and perhaps may or may not hint at the name of a specific house, when my ancestor's "Burnside" address was listed on immigration records, both to and from the UK, the Burnside part was in quotes, while the rest of the address was not. In other words, the address was listed as
" ' Burnside ' , Ardglass, Co. Down, Ire.".
Before living in Ardglass, a couple sons of John Halpin would list the actual address when traveling as "27 Rushfield Ave., Belfast".
My thoughts were this:
If more than one child of John Halpin would list his address as "27 Rushfield Ave., Belfast" while he resided there, and then later on, more than one child of his would list his address as
" 'Burnside', Ardglass, Co. Down" , then I was thinking this could be a local name or house name near some stream in Ardglass.
Based on your input, it seems like you may be thinking along similar lines. I'll have to look into this further.
Also, I did see that there was a Burnside road off of an Ardglass road, and it did appear to be in Co. Down, but it did not look like it was in Ardglass.