Does surface tension change with concentration?

Yes
#((dgamma)/(dc))_T= -(RTGamma_S)/c#
#gamma#=surface tension

Derivation
dG=#-SdT+VdP+gammadsigma+mudn_s#
At constant temperature and pressure,
dG=#gammadsigma+mudn_s# .............. (1)
#sigma#=surface area
n=no. of moles of the surfactant
#mu#=chemical potential= #((dG)/(dn))#

so,G=#gammasigma+mun_s#
#rArr dG=gammadsigma+sigmadgamma+mudn_s+n_sdmu# from (Gibbs-Duhem equation)...........(2)

by comparing the two equations (1) & (2) for dG, we get
#sigmadgamma+ndmu#=0 (Gibbs isotherm)

Now for an interface in which oil and water for example, are separated by a geometrically flat surface.The approximation implies that on the surfactant S accumulates at the surface and hence that #Gamma_(oil)# and #Gamma_(water)# are both zero.
The equation becomes
#dgamma= -Gamma_sdmu_s# where (#Gamma=n/sigma#)

for dilute solutions,
#dmu_s=RTlnc# WHERE c IS THE MOLAR CONCENTRATION OF THE SURFACTANT.

therefore at constant temperature, #((dgamma)/(dc))_T=-RTGamma_S/c#

I've tried to make the derivation look as simple as possible.If still not understood , leave a comment below.