  In the background of $f(R, L_m)$ gravity, this work investigates three
distinct dark matter halo profiles to test the possibility of generalised
wormhole geometry within the galactic halo regions. The current study aims to
accomplish these goals by examining various dark matter profiles including
Universal Rotation Curves (URC), Navarro-Frenk-White (NFW) model-I, and NFW
model-II inside two distinct $f(R, L_m)$ gravity models. According to the $f(R,
L_m) = \frac{R}{2} + L_m^\alpha$ model, the DM halo density profiles produce
suitable shape functions that meet all the necessary requirements for
exhibiting the wormhole geometries with appropriate choice of free parameters.
In addition, to examine DM profiles under the $f(R, L_m) = \frac{R}{2} + (1 +
\lambda R)L_m$ model, we consider a specific shape function. Further, we
observed that the derived solution from both two models violates the null
energy constraints, confirming that the DM supports wormholes to maintain in
the galactic halo.
