New Logo

If this is to be your personal logo to brand you as creative it should really show more inspiration. I'm not really getting a feeling that you created this with inspiration or research or sketching ideas on paper. The font isn't bad but it looks so thin next to such a heavy mark and the LT doesn't look like it's part of your brand name. It looks like the company name is "Design Z." This is your personal brand so take some time to do some research on what others have done, what works and what doesn't work. Really get inspired absolutely establish the discipline of starting on paper with a pen or pencil. Also, go without the shadow. That's a no no. Good luck and keep at it until you nail it!

Stacked option

I am not feeling this. The LT needs refined a bit. I include my signed initials in my logo as well. And I probably drew them close to a hundred times before I found the perfect one I could work with. And I mean drew- with a pen- and paper- NOT on the computer! And really, that's about how many times you can expect to draw them if you want something that doesn't look rushed.
As for the type, the Z stands out so much more than the rest. I read "design Z" . This needs a little more work.
Good start, just keep exploring ideas! AND SKETCH!!!!!