Excellent question. It’s best to have a graphic logo. You can include text with it if you like. An image can resize and always look nice, while a text logo can get cut off and run into other issues as screen sizes change. That’s one of the reasons why I suggest going with a graphic only logo.
What I would do is create a new graphic that incorporates your existing one and the text that you would use for your title. That will give you the best results overall.
If you run into any trouble or questions, let me know.