Why are linear phase filters called so, if they provide Constant delay instead of linear
Your premise is wrong. Linear phase filters offer linear phase.

Phase is not the same as time delay – at $f_1$, time delay $t$ will lead to a phase of $\varphi_1=-\omega_1\cdot t$, whereas at $f_2$, the phase will be $\varphi_2=-\omega_2\cdot t$ ($\omega$ is $2\pi f$); as you can immediately see, phase is a linear function of frequency.

(It's always good to remind oneself that frequency is just the derivative of phase over time, $\omega=\frac{d\varphi}{dt}$, and thus phase is just an integral of frequency over time.)