How do you assign (different) LaTex names to elements of a list?

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Say I have the following list of variables.

v = {(i,j): var("v_{}{}".format(i, j), latex_name="v_{{}{}}") for i in range(2) for j in range(2)}

How do I make it so that when I use the

show(v[0,0])

command, I get $v_{0,0}$ as output? I've tried stuff like

v = {(i,j): var("v_{}{}".format(i, j), latex_name="v_{i,j}") for i in range(2) for j in range(2)}

and

v = {(i,j): var("v_{}{}".format(i, j), latex_name="v_{{i}{j}}") for i in range(2) for j in range(2)}

but it only ever give me stuff like $v_{i,j}$ where it's just the literal symbols $i$ and $j$, not the entries of

v[k,m]

for some $k$ and $m$ I plug in, like 0, 0.