My wife and I are currently doing a lot of visiting in order to find a new Church Home, and I will be honest, we usually visit fellowships with Baptist in the name. We have tried a few Such and Such Christian Churches, and every one of them has been charismatic. So I think most people are going to go to a fellowship with Baptist in the name because of their doctrinal position, whereas a more generic name is likely to attract those who do not give too much attention to doctrine. Or the opposite, it will attract those who are "non-denominational," which usually means the fellowship is a denomination...charismatic.
But the bottom line is this, when people visit your Church they are either going to stay because of the Doctrine and Practice of the Church, or they are going to leave. That's how it usually works. The name really isn't a game-changer in my view, and might even give the opportunity to get some folk who usually go to non-denominational fellowships under some sound Theology.
In regards to the comments about "deceiving" people by being Baptist and not making that clear, I just don't see it. What I do see as deceitful are charismatic/pentecostal churches including Baptist in their name (i.e., Bible Believing Baptist, Holiness Baptist, etc.).
I will say this, though: when I was first saved and witnessing to people, often when people asked what denomination I was and I responded Baptist there were numerous times an acknowledgement that "Baptists know their Bibles." I think Baptists do stand out from other denominations, despite the fact there are so many different types, lol.
I will just say I hope it works out for you guys, and if your purpose is to serve God and preach the Gospel, God will reward that sincerity. So good luck with the name change, and remember, its not the name that makes the Christian.
God bless.