Is it permissible for a Muslim woman to say, for instance, "O my beloved ‘Umar," when mentioning one of the Companions of the Prophet, sallallaahu ‘alayhi wa sallam?

All perfect praise be to Allaah, The Lord of the Worlds.  I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

A Muslim's love for the Companions in general is obligatory. Loving ‘Umar in particular, is also obligatory. Therefore, it is permissible for the Muslim man or woman to say, "O my beloved so-and-so" upon mentioning ‘Umar or any other Companion. This indicates the Muslim's love for that honorable Companion and surely, whoever loves a people will be gathered with them on the Day of Judgment.

Allaah Knows best.