The Installer/Updater software ( setup-x86_64.exe, setup-x86.exe) can be downloaded here
website/downloadsite: http://www.cygwin.com/install.html

to start cygwin shell from windows the following program is used:

File name and path:     C:\cygwin\bin\mintty.exe
Product Name:           mintty
Internal Name:          
Original Filename:      

File Description:       Terminal
Company:                Andy Koppe / Thomas Wolff
Legal Copyright:        © 2013/2018 Andy Koppe / Thomas Wolff
Legal Trademarks:       
Comments:               

File Version String:    2.9.0.0
File Version:           2.9.0.0
Product Version String: 2.9.0
Product Version:        0.0.0.0

Version number displayed in the app:
use: c:\cygwin\bin\mintty.exe -V
mintty 2.9.0 (i686-pc-cygwin)

App-Icon in ICO format

cygwin is typically started using mintty, but with an additional icon parameter
In this way this Icon i used:

Regarding cygwin1.dll (as mentioned it is sometimes used in other packages), i

File name and path:     C:\cygwin\bin\cygwin1.dll
Product Name:           Cygwin
Internal Name:          cygwin1.dll
Original Filename:      cygwin1.dll

File Description:       Cygwin POSIX Emulation DLL
Company:                Red Hat
Legal Copyright:        Copyright © Cygwin Authors 1996-2018
Legal Trademarks:       
Comments:               

File Version String:    2.11.1
File Version:           2011.1.0.0
Product Version String: 2.11.1
Product Version:        2011.1.0.0

Version number displayed in the app:
use the following command in the shell:
$ cygcheck -s | grep ^cygwin
cygwin 2.11.1-1 OK

App-Icon in ICO forma