The saving seems a little bulky and non-personalized in Skyrim. In Oblivion, I could name saves. Is it possible in TES V? I would like to be playing
with more than one character at a time (i.e., 2 different games). But the saves seem linear in TES V. i.e. Skyrim 1, Skyrim2, etc. If I start a new game, do
I lose all progress in the previous game and revert to Skyrim 1, for instance? Thx for any help.

You could name saves in Oblivion? I thought that was one of the Morrowind features removed in Oblivion.

You can, exactly like an Oblivion.

If you're on the PC, then yes, you can name your save games by going to the save games folder and rename the files. Don't think you can do it from inside the game though, so may not be an option of you're on a console.

And no, if you do a new manual save, it won't overwrite a previous save, but autosaves will.

Correct
You can save named games in Skyrim and Oblivion using console commands on PC

Finally figured it out. Hit the ~ and, as in TESIV, I could savegame and name my game. Now, as you said, I can also ename in the save game folder. I DO with they had a Quicksave like TES IV. Thanks to all for comments. I "is" greatful.