When you send out an invitation, it should be understood that only the person(s) listed on the envelope are invited to attend. If someone wants to bring someone else along who was not invited, they should have the courtesy to ask first. This may be an uncomfortable situation, but if you cannot accomodate for the unexpected guest, then you are in the right to explain to them that the uninvited guest cannot come. However, if you want to avoid having to go through that, just let the other person come along, but you should still explain that the invited guest had no right to invite someone else on her own.