(Trudy, although we almost always agree, I must say on this we differ)
If they are the same person, then the two profiles should definitely merge. WikiTree is different than other genealogy sites - we are creating ONE profile for every person and ONE tree for all of us. We all work together on them (the Open Privacy level ones).
When I first joined WikiTree, I spent the better part of the first year straightening out the mess that was my mother's side in Connecticut. Almost all I did was work with existing profiles - adding sources and making sure everyone was documented and in their correct places in the family - and in the tree.
If you want to work on only YOUR tree, then it is better to do in a different program on your home computer. I haven't done that, but I'm sure others might have good suggestions for you, or you can search for subjects in the little search box at the top left of your G2G page.
Thank you for the question - really gets to the heart of things - and what makes WikiTree unique - and wonderful!