One Time Pad Key Distribution For multiple OTP keys, why not do this:

Key = Hash[(EC)DH Shared Secret + Counter]

The counter will increase per message, and the output of the hash will be random for each new unique input into it. What are the problems or weaknesses with this design??

EDIT:
For clarification: both parties will have the shared secret from an ECDH exchange, random numbers from Pythons os.urandom for generating the ECC key
This principle is commonplace, it is a key derivation from a shared secret. The academic thing to do is to use a Key Derivation Function or a MAC where hash of a concatenation is used, perhaps
$$\operatorname{HMAC-Hash}\;[\;\text{Key}=\text{(EC)DH Shared Secret},\,\text{Message}=\text{Counter}\;]$$

We call the output a derived key, and it can be a one-use key.

I would not call it a One Time Pad key, even if it is used only once to mask some payload with XOR, because the usual assumption is that a One Time Pad (key) is truly random, and this is only pseudo-random.