My Aunt sent me information regarding the name HaShem. Outside of prayer and Torah readings, this is what most Jews use when refering to God. It literally means "The Name".
She wrote: (posted with her permission)
Just wanted to give you a bit more information on use of God’s name. I’ve never heard any Jews use the word Jehovah and the ones I know would only consider that to be a Christian term being used. That’s pretty much along the same line as the article you referred to in your blog. I wanted to give you info on something they didn’t seem to mention.
What I’m familiar with is the use of Adonai in prayer, but in casual conversation they would use “Hashem” which means “The Name”. Ha = the and Shem = name. If you do a search on HaShem I’m sure you’ll have no trouble finding all kinds of references to it. It is one of the most common usages in casual conversation I’ve heard among Jews I’ve been around.
She also referenced the following:
"HaShem" - (both and neither masculine nor feminine and absolutely no plural); the word means, literally, "The Name," and it is the way that Jews refer to G-d when not in a Prayer or Torah Reading or Torah citation context. The reason is that the Torah forbids us from pronouncing the four-letter Name of HaShem in other than ritual contexts, and even then using only certain Names (other than the four-letter one, known as the Tetragrammaton) that embody characteristics, such as A-donai, E-l, E-lohim.
(Information from Judaism 101 at Orthodox Union)
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The link from yesterday's post regarding YHVH also included a short section about HaShem part way down the page, saying this is what most Jews use during everyday reference to God. Hebrew4Christians - YHVH
This is all very new (and interesting) to me. If you've found anything further, please let me know. I've done studies regarding the names of God before, but this was not covered during those studies.