Questions for booking a flight with a grandchild

I am planning a trip with my 10 year old granddaughter. All of the flights that I book are solo, so I apologize in advance if this is a stupid question. Since I am not the custodial parent (we do have the same last name), can I just book her together with my flight? I will not be using points if that makes a difference. Also, will there be issues going through security? I have TSA precheck so I know she can be included with me, but I assume we have to be booked together. TIA for any insight!