You can't right-click on the Recycle Bin and rename it Bit Bucket or Trash Heap. To enable rename or delete:

Hive: HKEY_CLASSES_ROOT
Key: CLSID\{645FF040-5081-101B-9F08-00AA002F954E}\ShellFolder
Name: Attributes
Type: REG_DWORD
Value: 40010020 default - can't rename or delete
Value: 50010020 enable right-click Rename icon option
Value: 60010020 enable right-click Delete icon option
Value: 70010020 enable right-click Rename or Delete icon option

If you want to delete the Recycle Bin icon, its safer to use TweakUI.

There is an inexpensive shareware version for Win9x, NT and Windows 2000 called Tweaki. From the shareware page:

Tweaki...for Power Users gives you all the usual Desktop management ability; like turning off animated windows, enabling auto logon, removing shortcut arrows, speeding up the Start Menu, showing BMP files as thumbnails in Explorer, editing the system owner/company information, placement of cascading menus off the Start Menu for Control Panel and the Printer's Folder, editing the file descriptions that Explorer lists for EXE, COM & DLL, turning on/off of AutoPlay, rebuilding the icon cache file, print directory structure as well as directory contents from within Explorer (Win9x only), disable smooth scrolling, making NT always boot with the Num Lock key on, changing the Windows NT logon logo to something you prefer, changing DOS box colors in NT, X-Mouse support in NT, Ghost connections in NT, disable autoexec parsing in NT, keep RAS connections alive, restrict remote registry access in NT, set max number of simultaneous users to your server, setting security within Win9x and NT, suppressing printer server notification messages, creating custom logon messages, allowing Ctrl + Esc to launch the Task List vs. the Start Menu, changing the directory where spool files are created to one that has more space, TAB in a DOS box under NT to complete path statements, tweak IP performance, change NT's default logon screen saver...the list goes on and on.