How to / is it possible to change Vendor Name in ESP8266-12E?
No. The Vendor Name is associated with the OUI.  The OUI is the first three parts of the MAC address.

The OUI's are all registered with IEEE here and Espressif's entries are:

18-FE-34   (hex)        Espressif Inc.
24-0A-C4   (hex)        Espressif Inc.
24-B2-DE   (hex)        Espressif Inc.
2C-3A-E8   (hex)        Espressif Inc.
30-AE-A4   (hex)        Espressif Inc.
3C-71-BF   (hex)        Espressif Inc.
54-5A-A6   (hex)        Espressif Inc.
5C-CF-7F   (hex)        Espressif Inc.
60-01-94   (hex)        Espressif Inc.
68-C6-3A   (hex)        Espressif Inc.
80-7D-3A   (hex)        Espressif Inc.
84-0D-8E   (hex)        Espressif Inc.
84-F3-EB   (hex)        Espressif Inc.
90-97-D5   (hex)        Espressif Inc.
A0-20-A6   (hex)        Espressif Inc.
A4-7B-9D   (hex)        Espressif Inc.
AC-D0-74   (hex)        Espressif Inc.
B4-E6-2D   (hex)        Espressif Inc.
BC-DD-C2   (hex)        Espressif Inc.
C4-4F-33   (hex)        Espressif Inc.
CC-50-E3   (hex)        Espressif Inc.
D8-A0-1D   (hex)        Espressif Inc.
DC-4F-22   (hex)        Espressif Inc.
EC-FA-BC   (hex)        Espressif Inc.


The ESP8266 does not advertise the vendor. The router / other device maintains a list of OUI to Name mappings (on Linux it's stored in /usr/share/ieee-data) and uses them to create a pretty display.

You would need to 


Change the ESP8266's MAC address somehow
Subscribe to IEEE and pay the relevant fees
Be allocated an OUI
Hope that every device in the world that would ever talk to your hardware updates its OUI mappings (which they seldom do).