Hi Balaraju,

Check the below link to hide the rename option you can check the current user and method in below link will hide the Rename Option but it's best practice 

https://community.servicenow.com/community?id=community_question&sys_id=a823c3e1dbd8dbc01dcaf3231f961956

Thanks
Chandu Telu
Please Mark ✅ Correct/helpful, if applicable,