How to politely request to be called by first name instead of Mr. Surname?

Let's say that somebody from a partner firm with whom I've never spoken before starts an email to me with "Dear Mr. Rossi,".

When a reply to her, I think I will then have to start with "Dear Ms. Her-Surname," to not sound disrepectful. But I would like to make this email conversation less formal next time.

Is there any better alternative to the sentence below?

Dear Ms. Her-Surname,

First of all, feel free to call me Ivo. Regarding your...

Solution 1:

Dear Ms. Her-Surname,

First of all, feel free to call me Ivo. Regarding your...

Solution 2:

I think that might be about as good as you can get in English. In some other languages, there are words for that, e.g. in Spanish, the verb "tutear" has roughly this meaning (spanishdict.com translates it as "to treat with familiarity"), which invites a degree of informality, and probably implies that the speaker wants the listener(s) to call him or her by a given name or nickname. English doesn't have different conjugations for the formal and informal second person, so it makes sense that there isn't one word for this.

If I were writing this, I would write it either exactly as you did "feel free to call me...", or possibly "please call me..." if I strongly prefer to be called by something. I think there is rarely a social stigma in American English to one person inviting the other to use an informal address—and the cases in which there might be, it's the kind of thing you usually know when you see it, such as talking with the president, prime minister, head of a company, etc.

Solution 3:

I received two phone calls recently from two non-native speakers, one from Poland and one from Pakistan.

I wrote to them “Please call me Dick”, so they called me — on the phone.

A non-native speaker myself, I have now switched to “Please call me by my first name.”