I am a graduate from Concordia College & University with a Doctorate Degree, my Student No. CCU 2008-08-21/441/PhD-TX. Is there a public registry whereby an individual can go online to see this list of Doctorate Degree learners?

I too am a Concordia grad. I don't think there is such a registry. (It would be private info.) Check with a Concordia dean's office to make sure.

Btw, have you ever heard the name Sam Goltermann? He was a past president of the Austin Concordia, 1956-1963.

First of course there are at least 3 concordia universities, so which one, in the US or somewhere else, and if in the US, what state.

I attended Concordia for the Seminary at one point.

But no most do not have online lists, if someone does a check, they do it officially though the registors office

First of course there are at least 3 concordia universities
I attended the Concordia near Chicago, had applied at the one near NYC in Bronxville and at the one in Ann Arbor, MI. There's one in Seward, NE, and one in Milwaukee. There's one in Austin, TX, too. More have popped up over the years. Many of them were mainly Lutheran teacher training, but have branched out into other disciplines. The Missouri-Synod seminary is Concordia, St. Louis.

so which one, in the US or somewhere else
The OP's registry number ended with "TX," so I'm guessing the Austin-Texas Concordia.