I have a J-link v8 and want to use it, but I can't find its name in Segger homepage, I want to know what ARM core it support and is it support BeagleBone or RPi.
The information you need should be on this page, the note at the bottom of the page refers to hardware revision 8 and up which I assume refers to the V8 you have.
In particular the following CPUs are supported: Any ARM7/9/11, Cortex-A5/A8/A9, Cortex-M0/M1/M3/M4, Cortex-R4, RX610, RX621, RX62N, RX62T, RX630, RX631, RX63N
While both the CPUs for the Beaglebone (Cortex-A8) and RPi (ARM11) are supported, I don't think that either board includes the JTAG port by default, you may need to solder pins on to make this available. Some information on the RPi here, the Beaglebone here.