After giving it some thought, here's what I would suggest for sgMAM:

• I would rename sgmam to simple_geometric_min_action_method following the style conventions of JuliaDynamics (alternative: we drop the _method in all functions we have defined)
• I would rename SgmamSystem(H_x, H_p) to HamiltonsTerms(H_x, H_p) or similar (can't think of a great name but it's not really Hamilton's equations and not the Hamiltonian either)
• It makes sense to write sgmam as a function of SgmamSystem, which I would interpret as a mid-level function. It would be great to have a function HamiltonsTerms(CoupledSDEs) that extracts the terms H_x and H_p from a suitable CoupledSDEs system, and then one could write a high-level function:

simple_geometric_min_action_method(CoupledSDEs) = simple_geometric_min_action_method(HamiltonsTerms(CoupledSDEs))

I suppose it would be some work to write the function HamiltonsTerms(CoupledSDEs) generally, so maybe we can leave that as an open issue and for now just

• rename the type/function
• explain in the docs that HamiltonsTerms is related to the underlying SDE via

Happy to hear your thoughts @oameye :)