General:
* Быть моим (byt' moim) - This is the most literal translation and is used in general situations.
With a specific object:
* Быть моим + object (byt' moim + object) - You would use this if you are talking about something specific. For example:
* "Быть моим другом" (byt' moim drugom) - To be my friend
* "Быть моим домом" (byt' moim domom) - To be my home
In the context of a relationship:
* Быть со мной (byt' so mnoy) - This translates to "to be with me" and is used when talking about being in a relationship.
Informal:
* Моим быть (moim byt') - This is a more informal way to say "to be my" and is often used in casual conversation.
Examples:
* Я хочу, чтобы ты был моим другом. (Ya khochu, chtoby ty byl moim drugom.) - I want you to be my friend.
* Этот дом будет моим домом. (Etot dom budet moim domom.) - This house will be my home.
* Я хочу быть с тобой. (Ya khochu byt' s toboy.) - I want to be with you.
* Хочешь быть моим? (Khochesh byt' moim?) - Do you want to be mine?
The best way to choose the right phrase will depend on the specific context and the level of formality.