[int_19h]

The sound [æ] is not entirely foreign to Polish and some other Slavic languages. It often shows up as an allophone of /a/ when it's between two "soft" (palatalized) consonants (e.g. the first /a/ in the word "niania"). The problem for us learning it is that it's not a separate phoneme, and worse yet, the environment in which it occurs in Slavic languages doesn't correspond to anything in English - and, conversely, in English it appears in environments where it could only be [a] or [ɛ] in Slavic languages.

The name itself is, of course, originally Roman, and it's also the name of many Christian saints, so basically every Christian country (not even necessarily a Western one) will be aware of it and have some version of it; for Polish that's be "Anton", I think, same as in Russian.

[stratocumulus0]

This doesn't happen in my speech, I certainly pronounce both <a>'s as [a] in "niania". [ɛ] is different, it certainly becomes [e] after palatalized consonants. I agree that people cannot tell the difference intuitively, though.

[int_19h]

It happens more in fast speech. If you draw out the vowel - as people tend to when they are trying to get a better feel of it - it will end up at [a] even if it doesn't start there. I suspect you'd need to actually record it and then look at the formants to tell for sure.