It should be probably be detectable as precisely the spell it is cast as, as a separate DC (increased due to the metamagic effects). However it should still be identifiable as the base spell with the normal DC.
I'm reading it as you just get the basic name of the spell, since the section on counterspelling doesn't mention metamagic except to say that metamagic doesn't change whether it can be countered. I wouldn't say metamagic "affects the name" of the spell. Spellcraft doesn't mention metamagic at all.
Heighten spell makes things a little interesting when you consider improved counterspell. Heighten changes the level of the spell, but metamagic specifically doesn't affect whether the spell can be countered, so could a caster with improved counterspell cast a 4th level evocation to counter a fireball heightened to 4th level (or higher)? I'd say you cannot do this, but that you do get the adjusted level so you can use your feat, but that might be a house rule or a table interpretation.
As this isn't in the PFS forum, I'd suggest to just give them the metamagic if they ID the spell (I'm assuming you're the GM). This is mainly in the interest of equality. A silent or stilled spell would be obvious (as the caster is not making noise, or gesturing), as would a quickened spell. So why not heightened, intensified, maximized, empowered, etc?
Unless you want to devise a system of DCs involving metamagic, which I think would be nice if it's a subsystem of the game that is expected to be used frequently, or is a level of depth you want to add to your game.