You cover a number of points here, I shall try to address each of them in turn.
Is it ok to delete the computer called USER from active directory?
It depends. If the old computer has gone, never to return, then probably. Bear in mind that once you delete it (or any object in AD) then you cannot get it back just by recreating a new object with the same name. Each object has a unique security identifier (SID) associated with it and it is this SID that is used when assigning permissions on ACLs, group memberships, etc. Just because a replacement object has the same name does not mean it will inherit the same permissions.
That said, for a standard domain joined workstation it's likely to have minimal impact. I would be more worried if this were a user or group object.
If you have referenced the old computer account in any ACLs, groups, etc. then once it has been deleted you will find that these references just refer to the SID and not the original computer name. If you come across any references that show a SID only then it it likely this is the cause (although not the only reason, so be warned!)
Renaming of computer accounts
You cannot rename a computer account directly from the Active Directory Users & Computers snap-in. The correct method of renaming a computer account is to do this client side. You should be logged in to the client with a user account that has full access to modify the computer object in AD (e.g. a domain administrator or alternate account that has been delegated the relevant privileges).
If you attempt to rename the object directly from within Active Directory then you will encounter trust relationship issues when you next try and use the computer.
This part is just my opinion, others may well have a different one.
I would never name a computer object with a name that is tied to a person (e.g. John Smith shouldn't have a computer named johnsPC). Instead come up with a sensible asset naming convention that you can use throughout your organisation (e.g. corppc123). Then when a computer asset is retired and replaced you don't have to worry about renaming the new object to be the same as the old; you simply replace it and move on.
However you go about naming and replacing your computers you need to ensure you keep items such as group memberships up to date (e.g. WSUS groups, SCCM groups, etc.). Also consider any scripts you have that reference computers by name, these will need updating (or better yet, changed so that they don't refer directly to PC objects). That's going somewhat beyond the scope of this question however!