To make a simplification, the ECVRF described in draft-irtf-cfrg-vrf-02 will use a key-pair $(x, Y=xG)$ and take an input $\alpha$. It will return $P = xH$, where $H = H_p(Y \mathbin\|\alpha)$, along with a Schnorr-based discrete-log-equivalence (DLeq) proof demonstrating that $P$ shares the same private key $x$ with $Y$ on generator points $H$ and $G$ respectively. This therefore proves that $P$ was correctly calculated as $xH$. $H_p()$ means to create a hash resulting in an EC point, which is what the linked document refers to as $\texttt{ECVRF_hash_to_curve}$. $G$ refers to a well-known base point for the curve.
You can create a modified $\texttt{ECVRF_prove}$ function for the purposes of generating a commitment. It will pick a uniform random blinding factor $b$, and will return $B = bG$ and $P' = x(H+B)$ instead of $P = xH$. It will return a DLeq proof that will demonstrate that $P'$ shares the same private key $x$ with $Y$ on generator points $(H+B)$ and $G$ respectively, and thus prove that $P'$ has been calculated as expected.
A modified $\texttt{ECVRF_verify}$ function will be created to verify the commitment. It will take $B$ as an additional argument, so that it can verify that the DLeq proof operates with the generator $(H+B)$ instead of $H$.
After this modified verification, it is known for sure that $P' = x(H+B) = xH + xB$. Since $x$ is private, the verifier cannot calculate $xB$ in order to determine the committed value $xH$. This also means it's impossible for a verifier to try to discover whether this is a commitment to any specific $xH$ value.
The commitment is opened by revealing $xB$ and providing a DLeq proof that $xB$ and $Y$ share the same private key $x$ on the generator points $B$ and $G$ respectively. Since we know for sure that $P'==x(H+B)$, and since we also know for sure that $xB$ is calculated correctly (due to the DLeq proof), we know for sure that we can calculate the correct value of $xH$ as $P'-xB$.
The $xH$ value which was committed to will be identical to the $xH$ value that would have been produced by the original unmodified $\texttt{ECVRF_prove}$ function.
Note that after the commitment is opened, we can only verify the value of $xH$ using the modified $\texttt{ECVRF_verify}$ function. If for any reason we need a separate proof that can be verified with the original unmodified $\texttt{ECVRF_verify}$ function, this additional proof can be provided by the prover at the same time that the commitment is opened.