Can my boyfriend take the phone that he bought me?

While there are some rare exceptions (including, in some states, a gift in contemplation of marriage, like an engagement ring), the general rule is that once a gift is given, the giver loses all rights in it, so that if your boyfriend gave you the phone free and clear, with no conditions, he can't now take it back.  The problem is proving it.  He may claim, for example, that he didn't give you the phone,but only  loaned you the phone to use while you were together.  I assume that you have nothing in writing to prove what happened, so that if the matter went to court, it might wind up being his word against yours.