There is one good reason not to do this as it is not allowed by the FCC.
The Technician, General and Exam liscenses are access to privileges. You must take each exam.
"To upgrade to General Class, you must already hold a Technician Class
license (or have recently passed the Technician license exam)."
In terms of vanity call signs and what is available you can start here: arrl.org/vanity-call-signs and arrl.org/applying-for-a-vanity-call. Does that help? – KG5HNZ 8 mins ago
Look at this chart and you'll see why it makes sense to be licensed in the three Classes.
Further, there are other rules and regulations that you must be aware of as a holder of a Technician, General and Extra licenses.
When taking the Technician Class Exam, if you pass you are given a chance for free to attempt the General Class exam. Upon passing the General Class in turn you can take the Extra Class Exam, for free. This provides you with all privileges that are available to you.
I've seen this done and its quite possible.
Call signs have changed recently, so its best to goto the ARRL site to read up on the changes. Honestly, just get your license before you start thinking about changing your call sign, that essentially you don't have at the moment.
In terms of vanity call signs and what is available you can start here: arrl.org/vanity-call-signs and arrl.org/applying-for-a-vanity-call.
If you feel you are ready for the General Class then try the tech mock exams on the internet and see how you do...
Hope that helps.