A valid nickname for [name_m]Leonidas[/name_m] could be [name_m]Leonid[/name_m], even though it’s the Russian name? I like it a lot; I don’t really like [name_m]Leo[/name_m].
I guess it works, but it’s not my favourite. [name_m]Leonid[/name_m] is still very long and feels like a name on its own, it doesn’t have that friendly, short & cute or casual feel that nicknames are usually for. I’d also pronounce [name_m]Leonid[/name_m] and [name_m]Leonidas[/name_m] differently but maybe that’s not an issue for you if you pronounce them the same way? Personally, if you like [name_m]Leonid[/name_m] I’d just use [name_m]Leonid[/name_m] on its own instead of [name_m]Leonidas[/name_m].
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Personally I second @tallemaja thoughts, it does feel a little long for a NN, & that if you prefer that name it might be worth considering it as the FN instead.
Overall though yes it could work.
Other NN ideas could be: [name_m]Leon[/name_m], [name_m]Lenny[/name_m], [name_m]Lonny[/name_m], Idas, Daz 
It could work. It does feel a bit like a separate name, but if it emerges and feels natural for a [name_m]Leonidas[/name_m], it could work
Like one user said above, I would also pronounce these two names differently, so one being a nickname for the other does not personally make much sense to me. Would you consider [name_m]Dino[/name_m] (either dy-no or dee-no) as a nickname?