The word "maiden" (at least in the UK) is now essentially an obsolete word. It's not that anyone would find it particularly offensive, so much as it's basically not used any more. (As with other obsolete words, it's occasionally used for irony, so you might jokingly refer to somebody as a "fair maiden", but the intent is humoristic rather than to cause offence.)
But, as is often the case, this obsolete word survives in the fixed phrase "maiden name", which is still perfectly common in British usage. I don't think anyone finds it offensive-- it's just an administrative term, and the word "maiden", offensive or not, is as I say to all intents and purposes no longer used anyway. People are generally familiar with the term because it's very very common for banks to ask you, for example, what your "mother's maiden name" is.
However, as English is an international language, now spoken by more non-native than native speakers, there's also a move to try and avoid obscure terms, or deliberately choose alternatives whose meaning is more obvious to speakers of other languages. So it's possible we may see a move towards alternatives such as "Family name before you were married".