Hi again,
1) I would like ask why program execute both strings if I only pushed "name1Str" to be printed ?

2) How can I make that string, could be printed few lines lower, keeping empty space upper?

Your string needs to be terminated with a zero byte:

Ohh, thanks.
Do you know maybe how about second point?
How to tell "print this sting few lines lower?"

Maybe:
down1 db 13,10,0
down5 db 5 dup(13,10)
db 0

push down5
Call [printf]

Thanks Roman it's works.
btw. what's mean this numbers? 10, 13, 0.
I saw if I put another number like 11, 12, 0. On my string I got some extra symbol or any kind of weird signs.

See here for the meaning of the control characters.
https://ascii.cl/control-characters.htm

13 = CR, 10 = LF, etc.

is there any book about assembler worth recommending?

IMO, books need assembly but assembly dont need books

I dont think there are very good content in modern books (and old books will teach you 16-bit assembly and in real-mode), but I suggest you read manuals.

- fasm manual (obviously to know more about fasm features)
- your OS api (maybe win32.hlp file)
- target CPU manual (assuming you have intel CPU, then you gonna need intel's software developer manual)
(just search intel sdm)

This book seemed decent (covered FASM programming and even had a section on making .Net integrations): https://www.packtpub.com/product/mastering-assembly-programming/9781787287488

And I used it to complement the video series on FASM: https://www.udemy.com/share/101Wo2BUMSdVpVRHo=/