This turns out to be unclear in the rules, and there are no official clarifications. However, there are at least three interpretations I've seen used, two of which I think our very reasonable and one I understand but do not think is actually well justified.
Interpretation One: generic beast of a type in the Monster Manual
I'm putting this one first, even though it's the one I like the least. The ruling here is that you choose a listing from the Monster Manual (or other accepted official source of beast stat blocks) and become a generic, average example of that beast. There's no room for customization, and you can't ask for an animal that exists in the world that does not have a stat block. By this ruling, you can't choose the size of the elephant form you assume.
I don't like this because the Monster Manual explicitly says:
Other Animals: A book of this size can’t contain statistics for every animal inhabiting your D&D campaign world. However, you can use the stat block of one animal to represent another easily enough. For example, you can use the panther statistics to represent a jaguar, the giant goat statistics to represent a buffalo, and the hawk statistics to represent a falcon.
... which at least implies that "reskinning" should be an option, and of course there's the whole "Creating a Monster" section of the DMG — this isn't supposed to be a game limited to those pre-made stat blocks. However, I have seen this interpretation many times and particularly in Adventurer's League play, where DMs don't want to have to deal with possible outside-the-box thinking. As written, the feature is very open-ended, and this is an easy simplification.
Interpretation Two: exact creature you've seen
This is a pretty straightforward literal reading. The rule says:
Starting at 2nd level, you can use your action to magically assume the shape of a beast that you have seen before.
... and by this ruling, you must have seen the exact form you want to take. If you want to be an elephant, it needs to be the form of that particular elephant you saw out on the savanna on your journey there three years ago. By this ruling, you may be able to have a variety of elephant forms at your disposal, depending on your character's history.
The funny thing is, despite how straightforward this is, I have only seen the 5E druid played this way once, and that was because the player wanted to — they'd tell the story of the time they met this giant crocodile as they'd shift into that form. And they made a big deal of keeping a journal of beasts encountered in the campaign. But the DM for this game wasn't enforcing this at all — they very certainly would have allowed (and maybe sometimes preferred, when it got to be a bit much) a more loose interpretation.
Interpretation Three: seen one, seen 'em all
This is the most free interpretation, and in my experience the one most long running non-public-play games go with. Here, if you've seen an example of a beast, you now have unlocked the general category of "elephant", and can take an elephant form colored by whatever detail you like (much like a spellcaster assuming a different humanoid form with alter self). By this ruling, you can pick any size you like within the "huge" category.
Usually, this is also different from Interpretation One in allowing you to choose a totally different type of elephant with a custom stat block, as long it's reasonable to have encountered that alternate type and the DM agrees. This could be the difference between the real world's Asian and African elephants, or it could be "Juvenile Elephant" (size large, or even medium).
This idea isn't without backing in the rules; cribbing from my earlier answer to a related question, Xanathar's Guide has a section named "Learning Beast Shapes", which doesn't resolve this issue, but does casually mention:
The tables include all the individual beasts that are eligible for Wild Shape (up to a challenge rating of 1) or the Circle Forms feature of the Circle of the Moon (up to a challenge rating of 6).
... emphasis mine. The table does not, actually, list "Bessie, the mule from Farmer Grumwold's place up near Meadowville" as an "individual beast". It lists "mule".
This supports the idea that intention behind the rules is that "a beast" means "a type of beast", not actually a singular, individual beast.
There is no conclusion. :) You'll need to decide this at your table.
In a game that I ran, I had a druid who wanted to only specialize in dinosaur forms, but there turn out to not be as many of these as is representative of real-world dinosaur diversity, and some of them are weaker than traditional standby druid bear and wolf forms for no real reason. So I let that player come up with a whole suite of different dinosaurs at each CR, and made sure they seemed reasonable with the CR rules in the DMG (plus comparisons with other beasts at the same CR). This turned out perfectly well: their theme was fulfilled and they were happy.
It sounds like you have a theme idea going on with your loxodon. This is awesome. Were this my game, I would absolutely encourage you to have a selection of elephant and elephantine forms available to fit all of your Wild Shape needs.