The decision will in the end rest with your publisher, so I suggest you address the question to your editors—that’s what they’re paid for, and they will probably appreciate your calling their attention to the problem. In fact, the standard authority in my own field, MLA Style Manual and Guide to Scholarly Publishing, although it does not directly address this question, does say of spelling variants in general that you should “inform your editor, before copyediting begins, of any necessary deviations” from the practices MLA otherwise recommends. (3.4.1)
MLA also says “If the name of an author whose works you used appears in various spellings in the works (e.g., Virgil, Vergil), consolidate all the entries for the sources under the preferred variant in your works-cited list (6.4.3),” and it specifically distinguishes this from the need to list separately works written under natal and married names.
My reading of these suggests that you employ the version with the ‘long’ umlaut throughout, with a note at each relevant works-cited entry of the variant spelling under which it was published.
And Oh, yeah: in the works-cited list (but not the body of your text) Prof. Szegő should appear as Szegő Gábor, with no comma: Hungarian, like many East Asian languages, puts the surname first.
You can certainly assume that English speakers will omit the tone-denoting diacritics in the Vietnamese versions of the names of people and places — partly because they don't understand what they signify, and partly because they would have no idea how to reproduce them even if they wanted to — and that most of them will be confused about the different conventions regarding the order of names in conventional Vietnamese versus English usage.
However, the name Ho Chi Minh is so well-known to speakers of English that it has become fixed in that form, and is therefore probably immune to the reordering of its elements.
Where Vietnamese place names consist of several discrete elements (e.g. Việt Nam and Hà Nội), it seems to me that English speakers prefer to run them together, as you have already observed.
I suspect the greatest influence on all aspects of how native English speakers treat Vietnamese names is the way they are presented in newspapers, although the easier access to information about Vietnamese culture that has been made possible thanks to the Internet may prompt a few English speakers to try harder to conform to at least some of the Vietnamese norms.
You might also find some of my remarks in this discussion relevant.
Best Answer
A common convention for indicating a call-name is to put it in quotation marks (or sometimes in parentheses) immediately after the legal given (first, in English-naming traditions) name. This works for nicknames and completely un-related call-names as well as middle names. For example:
In the case of middle name-as-call name, it's common to put the middle name in quotes after both first and middle legal names:
This form (Firstname Middlename "Callname" Lastname) also shows up for nicknames sometimes, especially where the full name is probably completely unfamiliar:
On the other hand, the form Firstname "Callname" Middlename Lastname is sometimes used when the call name is a nickname that is clearly derived from the first name:
Again, these examples can be found searching for likely examples, such as "katherine katie grace" or "margaret maggie jane", both of which will find numerous obituaries.
None of this is set in stone; whether you use single- or double-quotation marks or parentheses, and whether you put the call name between first and middle, between middle and last, or between first and last (omitting the middle) are all style choices. I would recommend repeating the middle name when it is the call name, though, for clarity's sake.