I keep the same name as I change SIBs... just makes it easier. I had a GRP trailed boat years ago that came with its name of Nimrod so made my SIBs as if its tender... Nimrod II.
Of course you need to be careful and appropriate with names... I associate mine with "Mighty Hunter" as in the Nimrod aircraft... but in a thread a while back on the dangers of naming an esteemed Mod was quick to point out the USA meaning to be an "inadequate person".
If I find myself in the USA with the SIB I'll be well lost so sticking with it!
See here... Some help with her name...