Why would Mike give the German engineers his real name? When the head German engineer and Mike are talking in S4E7, the engineer tells him the meaning of 'Ehrmantraut' - This seems sloppy after all the trouble they go through to hide the location of the facility. Are they planning to kill them all anyways?
I have a few possible theories:
1) Mike trusts the head guy. I don't know that any of the other workers overheard Mike's real full name being used, but I could be wrong.
2) Finding someone only by their name, even an uncommon name, is no easy thing. It's not like he shared his social security number, and I doubt in this world you'd be able to type Mike Ehrmantraut into google and find a hit that's our Mike. If you did, it might be his listed employer, and good luck finding him that way.
3) Mike has Gus to back him up. I'm sure the guys hired here are aware of the monumental amount of wealth and therefore power that Mike's boss must have.
4) Mike's a former cop, I dont think much scares him. Especially if he can stand up to Fring.
It is sloppy and out of character for Mike.
Bottom line, there is no reason to tell the guy his real name. They were talking in a bar; there are dozens of things to talk about that don’t involve giving his name. As an ex-cop, Mike should know how to carry a conversation while withholding things.
While there is no reason to tell his name, there are lots of reasons not to. Once he gives it to the head German, he should assume the other Germans will learn it. If one of those Germans gets caught for something else or develops a grudge, or just shoots his mouth off at the wrong time, then the authorities have a name and a general location to associate with what is obviously a secret underground facility for nefarious purposes (drug lab would be any cop’s first guess). The cops running a search on Mike Ehrmentrout in the Southwest, with a description and approximate age, wouldn’t have to sift through many DMV records to find their guy.
The fact that Mike later releases the rest of the German workers, all of who have good reason to hold a grudge against him (he killed their friend) is exactly the reason to make sure they know as little as possible about him. You’re right. This was dumb and very much out of character for the smart, deliberate, and careful character that Mike usually is.