Who invented the term "Coulomb logarithm"? Who is the author of the term "Coulomb logarithm"? In fact, Coulomb logarithm was computed by Langmuir in his paper of 1928 where the term "plasma" was introduced into physics, but the term "Coulomb logarithm" seemed to appear later. The earliest reference I found is the paper Relativistic kinetic equation  by Belyaev & Budker (1956).
UPDATE: Using Google Labs I found a reference dated by 1937 in very rare Georgian journal in Russian.
 A: Interesting question.  I believe that the term "Coulomb logarithm" was first used by Landau in a 1936 paper, "Die kinetische Gleichung für den fall Coulombscher wechselwirkung," which was published in the German-language journal Physikalische Zeitschrift der Sowjetunion.
It is difficult to prove a negative, so I cannot claim to be 100% certain that there are no earlier sources.  However, as evidence, here is a quote from the classic 1976 monograph "Theory of plasma transport in toroidal confinement systems" by Hinton and Hazeltine (emphasis added):

All of the transport literature under review is based
on the assumption that the distribution function $f_a(\mathbf{\overrightarrow x}, \mathbf{\overrightarrow v}, t)$
satisfies the Fokker-Planck equation,
$$\frac{\partial f_a}{\partial t} + \mathbf{\overrightarrow v} \cdot \mathbf{\overrightarrow \nabla}f_a + \left(\frac{e_a}{m_a}\right)(\mathbf{\overrightarrow E} + c^{-1} \mathbf{\overrightarrow v} \times \mathbf{\overrightarrow B}) \cdot \frac{\partial f_a}{\partial \mathbf{\overrightarrow v}} = C_a(f), \tag{1.1}$$
where $e_a$ is the charge and $m_a$ the mass of particles of species $a$, $\mathbf{\overrightarrow E}$ and $\mathbf{\overrightarrow B}$ are, respectively, the (macroscopic) electric and magnetic fields, and $C_a$ is the Fokker-Planck collision operator:
$$C_a = \sum_b C_{ab},$$
$$C_{ab} = -\frac{2\pi e_a^2 e_b^2}{m_a} \ln \Lambda \frac{\partial}{\partial v_\alpha} \int d^3v' \left[ \frac{f_a(v)}{m_b} \frac{\partial f_b(\mathbf{\overrightarrow v}')}{\partial v_\beta'} \\- \frac{f_b(v')}{m_a} \frac{\partial f_a(\mathbf{\overrightarrow v}')}{\partial v_\beta'} \right] U_{\alpha\beta} \left(\mathbf{\overrightarrow v} - \mathbf{\overrightarrow {v'}}\right) \tag{1.2}$$
Here, a sum over repeated Cartesian indices $(\alpha, \beta)$ is implied and
$$U_{\alpha\beta}(\mathbf{\overrightarrow x}) = x^{-3}(x^2 \delta_{\alpha\beta} - x_\alpha x_\beta) \tag{1.3}$$
The Coulomb logarithm is formally given by
$$\ln \Lambda = \ln (9N) \tag{1.4}$$
where $N \gg 1$  is the number of particles in a sphere of radius $\lambda_D$, the Debye length. Equation (1.2) was first derived by Landau (1936). Chandrasekhar (1943) used a different argument to derive a special case of Eq. (1.2), which was later extended, somewhat, by Cohen, Spitzer and Routly (1950).

Also, here is a quote from a 2013 paper, "Effective Potential Theory for Transport Coefficients across Coupling Regimes":

The bare Coulomb potential neglects screening of the intervening medium and leads to a divergent collision operator. To fix this unphysical divergence, Landau utilized the weak coupling assumption to cut off the impact parameter at the Debye screening length [3], hence, imposing an effective potential. This approximation leads to the traditional Coulomb logarithm, $\ln \Lambda$, where $\Lambda \sim \Gamma^{-3/2}$ is the plasma parameter. It is valid in the limit that this parameter is asymptotically large.

