Hi Venkatta,
Thank you for posting in our forum
>>>Is it possible keep domain name and NetBIOS domain same,Is trust relationship can be created between domains.
You cannot delegate the creation of trusts to any user who is not a member of the Domain Admins or Enterprise Admins groups. Even though you can grant a user the Create TDO (Trusted Domain Object) right or the Delete TDO right in the System container of a domain, the user will not be granted the right to create a trust.
When you are logged on locally to a domain controller and you try to create a new trust by using Active Directory Domains and Trusts, the operation may be unsuccessful and you may receive the message “Access denied.” This issue occurs only if you are logged on locally to the domain controller as an ordinary user (meaning that the user is not logged on as Administrator or as a member of any administrative groups for the domain). By default, ordinary users are blocked from logging on locally to a domain controller unless Group Policy is modified to permit this.
Give you an article, the content of the article is more detailed, you can refer to the link below:
Hope this information can help you
Best wishes
Vicky