This is related to Kodaira's Complex Manifolds and Deformation of Complex Structure Chpt 2, Sec 2's Hopf Manifold example.
Consider $W=C^n-\{0\}$, $a=(a_1,\dots, a_n)\in C^n-\{0\}$ with $|a_i|>1$. $a$ acts on $W$ by multiplying individual components. Then $G=<a>$ is the multiplicative group generated by $a$. Clearly $W/G$ is a complex manifold. Pick $f$ meromorphic function on $W/G$ and lift it to $W$.
$\textbf{Q:}$ The book says the function $f$ defined on $C^n-\{0\}$ extends to $C^n$ by Levi Extension Theorem.(I guess this $f$ does not have to be $G$ equivariant for extension purpose.) Consider $n=1$ and $exp(1/z)$ which can never be extended to $C$ as it has infinite order pole at $z=0$ but local germ at $0$ is always quotient of 2 polynomials up to invertible elements. So $n\geq 2$ or does $f$ require $G$ equivariance?
Yes, it should be assumed that $n\geq 2$. The Levi extension theorem only applies in dimensions $n\geq 2$. When $n=1$, there are always lots of meromorphic functions on a Hopf manifold (indeed, it is an elliptic curve).