Does a possession's preposition changes according to who owns the item in Spanish?

The gender of the noun does not change depending on who happens to own that noun. The preposition you would use for that noun always agrees with the noun, NOT with the gender of the person who owns that noun. SO you would use "Le la doy", even if the shirt happens to belong to a male. The indirect object pronoun in the third person singular in "LE", by the way, not "SE".