As I understand the situation, the name on the Global Entry card (and on your passport) is spelled, say, Mc Cool but in your Mileage Plus’s account and on the ticket it is spelled Mccool. You were able to change your Mileage Plus account to read McCool but they will not add the space. And your concern is that you will be denied Global Entry because the name on your boarding pass (which will be the same as the name on the ticket) and the name on your Global Entry Card (/and your passport) do not match exactly. Is that it?
Maybe this will help. Global Entry only applies when you return to the US from abroad—-it helps speed you through immigration. It also gets you PreCheck with TSA upon your departure from the US (not within Europe).
I don’t see any issue with using the Global Entry system when you go through immigration upon return to the US—-no one ever looks at your boarding pass. For that matter, they do not look at your Global Entry card either. Global Entry is attached to your passport, and when you place your passport on the reader screen at the immigration gates the machine will recognize it. Here in Seattle, the machine then takes your photo and tells you to proceed to the Global entry line. We did show our passports to the CBP agent there, but he asked no questions and we did not have to do a customs declaration. It was all very quick.
It may be slightly different at other airports (this was brand new in Seattle, and other airports may still be in the process of updating their systems) but in any case your boarding pass is irrelevant. The agent mis-spoke when he told you that you would be “denied Global Entry” if the passport name and the name on the boarding pass did not match exactly, and that the missing space after Mc is the problem. As others have noted, the space between names is often eliminated from the printed boarding pass ( my first and middle names are always run together.
On the other hand, the name discrepancy might possibly keep you from getting TSA Pre on your boarding pass, because that will conform to the name on your ticket, which I believe you said is Mccool. And in theory at least you could have trouble with boarding the plane because of the misspelling, but you did not mention that as a concern (and I believe you said the United rep said not to worry).
You have corrected the spelling somewhat in your Mileage Plus account, to McCool, but there is still no space. But it is the name on the ticket (the one you used when you made the reservation) that will be on the boarding pass, not the corrected name on your Mileage Plus account. To my understanding, it is the actual spelling on the boarding pass, including capitalization, that must match the passport. Spaces are irrelevant—-the airlines run names together (usually first and middle) on the boarding pass as a matter of course. I don’t know if it is to save space or to prevent alteration of the boarding pass, but that is what they do.
For your peace of mind, you might call United back and see if they will re-issue the ticket to conform to the spelling that is now on your Mileage Plus account, with the second capital letter following the Mc (so McCool in my hypothesis). As long as the ticket is for a United Airlines plane, not a partner, they should be able to do that ( maybe for a fee).