"Mon" is linked to the noun that follows, not to the gender of the person talking.
Léa says: "My (masculine singular) brother is called Tom" (Mon frère s'appelle Tom.), because brother (frère) is a masculine word.
Tom says: "My (feminine singular) sister is called Lea" (Ma soeur s'appelle Léa.), because sister (soeur) is a feminine word.
SummaryThe French translation for “my (masculine singular)” is mon.
Examples of "my (masculine singular)" in useThere are 82 examples of the French word for "my (masculine singular)" being used: