"I need to update the public tree but I do not see where you can upload a new GEDCOM to an existing tree."
Nope. You can't "merge" a gedcom into an online tree.
"If I upload a GEDCOM and use the exact same name as my old tree will it replace the old one or will there now be two trees with the same name."
No, it won't...and you'll probably wind up with 2 identically named trees (not sure, just guessing). Just name it something different and rename it once you've deleted your old tree...or delete your old tree first and the issue becomes moot.