Yes, you can get your name embroidered on the carry bag, but you will have to order it embroidered.  They can't embroider it after purchase.

so that means I have to special order it from a authorized titleist dealer and what is the extra cost, will all titleist dealers do this for customers?

Yes, you will have to special order it through an authorized Titleist pro shop or retailer and although all shops can place the order, you will have to check with the individual store.  There is a five week lead time and pricing is up to the pro shop or retailer.

I work at a course and we can order bags for our customers, because I am gonna order a 2013 Titleist bag as soon as I can. I like the new green apple color bag, it will be very catchy and look nice with my name embroidered on it.  Good luck with your search, hope you get just the one you are looking for.