Basically nothing. The Star Trek Encylopedia listed named ships but that predated DS9 when we started seeing huge fleets deployed with no names.
The numbers in DS9 seemed a lot but I don't know. The Federation is supposed to span 8,000 light years or something like that. Which is a lot of space to patrol etc. I think it was just part of upscaling the size of these powers to portray just how big and devastating this War was supposed to have been. I think they tried to not let it get too unbelievable. A bit like how with one exception they tried not to have any Starbase numbers higher than 500 so as to avoid it looking like they had too many. But to be honest I have to say I don't find the idea of a fleet in the low thousands too much of a stretch given the broad range of duties.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist