The joys of having a severe social phobia whilst being extremely introverted mean that I don't eat in restaurants etc.. so those are not situations I'm in.
I've actually had a good think about this before replying & I truly don't see what is strange about wanting to be called my given name.
I wouldn't be having a conversation with staff in a shop or restaurant anyway, I'd just place my order, use my ps & qs when required & leave a tip if appropriate.
None of it requires knowing the name of the person working there.
I don't see well enough now to read a name badge so I wouldn't even notice it was there.
If I go into a shop with pushy staff, they don't know my name so they just say 'can I help you?' & I respond yes or no but no names get used.
I don't phone people apart from my mother once a fortnight (if I didn't she would complain) & I honestly can't recall the last time I needed to phone a company about anything.
If I was getting a piece of furniture delivered or similar they phone & ask for Miss S. which is the name on the order.
Last week I had to online chat with a software company I use & they didn't call me anything, just said "my name is x how may I help you?" I didn't call them anything either because their name is not relevant to my tech issue.
They knew my name from my account but they didn't use any variation of it at all.
When a delivery driver or the postman knocks on the door they ask for Miss S. because that is what is written on the parcel.
I've lived next to the same neighbours for eleven years now.
They say hello if they see me when I'm outside but we don't know each others names.
I do know her first name because her ex used to scream it in the street quite often but I haven't ever used it.
I'd call my boss Mr/Miss/Mrs if I had one, but have been s/e & worked mostly alone for most of my life.
When people want something from you they call you whatever you want without complaint I guess, so my customers never seemed to have an issue.
My doctor, optician etc... has always called me Miss S if they called me anything.
Nurses, midwives etc... seem to think they can use your first name but desist when asked not to.
Teachers called me Mrs S as they seem to assume every woman with a school aged child is married.
My own teachers at school called me Miss S & all the other girls the same (girls only school)
I really just don't come across people who call me anything else.
Maybe because if you asked me my name I'd say Miss S because it would not be in a social situation.
I am almost never in them & if I have to be I'm not there to socialise, I'm there because I'm obliged to be for some reason.
If you responded giving your name as Mary I'd either ask for the rest of your name & use that or not use your name at all in the following discussion.
People tend to respond in kind though, so I say Miss S & they say Miss Whatever.
If I had to correspond with you at a later date I'd ask for the rest of your name & use that.
If you didn't give me a Miss/Mrs I'd use Miss (or Mrs if you were wearing a wedding ring & I'd noticed) & if it isn't correct you'd either never mention it & keep getting called that or respond with it's Ms or Mrs & I'd use the one you preferred instead.