If unsaved people make their way to my church on Sunday morn, the church is not going to change its name. The Christians within will no doubt reach out to the visitors, welcome them in, fellowship, answer questions, etc. No need to change the name when all they are doing is being Christians and doing what God instructs Christians to do. Love one another.
I vote Option 1 without the name change.
My question to you all: What are you afraid of?
Your little sanctuary was not defiled. Visitors come and go, and yes there may be a 'problem child' occasionally cross the threshhold. It's a threshhold of membership that some of you consider sacred, but that *God* does not.
Love one another. Sit with those tax collectors as Jesus did.
The problem isn't with the site or its vision. It is the pride and fear of the members.
Have a blessed day.