Initially pulsars were named with letters of the discovering observatory followed by their right ascension (e.g. CP 1919). As more pulsars were discovered, the letter code became unwieldy and so the convention was then superseded by the letters PSR (Pulsating Source of Radio) followed by the pulsar's right ascension and degrees of declination (e.g. PSR 0531+21) and sometimes declination to a tenth of a degree (e.g. PSR 1913+167). Pulsars that are very close together sometimes have letters appended (e.g. PSR 0021-72C and PSR 0021-72D). The modern convention is to prefix the older numbers with a B (e.g. PSR B1919+21) with the B meaning the coordinates are for the 1950.0 epoch. All new pulsars have a J indicating 2000.0 coordinates and also have declination including minutes (e.g. PSR J1921+2153). Pulsars that were discovered before 1993 tend to retain their B names rather than use their J names (e.g. PSR J1921+2153 is more commonly known as PSR B1919+21). Recently discovered pulsars only have a J name (e.g. PSR J0437-4715). All pulsars have a J name that provides more precise coordinates of it's location in the sky.
For want of a better convention, the pulsar pages here will use the epoch 2000 convention. For example, the Crab Pulsar page redirects to PSR J0534+2200. Some of the objects discussed on this site are neutron stars for which pulsation have not been detected; for these we use the most astrometrically accurate name, usually the Chandra designation, e.g. CXO J232327.8+584842 for the compact central object in the supernova remnant Cassiopeia A.