on a first-name basis

Adverb

idiomatic not-comparable

(idiomatic) Having enough familiarity with another person to call them by their first name, as opposed to their surname.

Japanese Meaning

名前で呼び合えるほど親しい関係である / 親しい間柄において、相手をファーストネームで呼ぶ関係にある

いくつかのプロジェクトで一緒に仕事をした後、カレンと私は下の名前で呼び合うほど親しくなったので、丁寧な敬称を使わずにメールをやり取りすることが多い。

Sense（1）

(idiomatic) Having enough familiarity with another person to call them by their first name, as opposed to their surname.

We are not yet on a first-name basis.