My surname’s Scandinavian – as is my heritage – but somewhat unusual because it’s monosyllabic and very short.
When pronounced phonetically according to American English convention – Scandinavian pronunciation would involve vowel sounds we just don’t use here – it totally sounds East Asian.
So my surname ends up being actively misleading to lots of people who are making assumptions about my heritage.
I recently took on a Korean client who I could guess was disappointed that I wasn’t Korean – or at least Chinese or something! – once we met in person. (Her facial expression when she answered the doorbell, along with her later comment that my surname “sounds Korean,” made me think that.)
(To be clear: since I was tutoring her first-generation Korean-American child, I’m not particularly offended that she was probably hoping she’d found a Korean-American tutor. Rapport is important in that kind of relationship, and speaking Korean would have been a bonus – as would having experienced the US as an Asian-American generally. It wound up being a good tutor-student-parent relationship.)
I get why the OP felt they must share, in other words. Surnames sometimes give good information about a person, which is why people pay attention to them; but they can also give incomplete or misleading information, which leads to problems.
I don’t think there’s anything wrong with merely being curious about where someone’s name “comes from;” curiosity is only human, and can be satisfied without being disrespectful. On the other hand, there are less innocent reasons to want to be able to make a reliable guess about someone’s heritage/ethnicity from their surname.