how much noise figure should a LNA be?

how much noise figure should a LNA be?

I mean, how much noise figure should it be at most if the amplifier can be called a LNA?

3dB?

Depends on application, frequency band, bandwith.
Most LNAs have NF < 3 dB if operated from UHF to say 30 GHz, and a moderate bandwidth of say 1 GHz.
Ultra-wideband LNAs are e.g.those operating from 1 MHz to 40 GHz where NF < 6 dB is considered low.