Hi @Mohit Madan - Thanks for reaching out.
If you have blob present in the storage and accessible over browser, I believe you are having the access level of the container set as Blob as a result the blob can be accessed anonymously. The recommendation is that you can change the access level to Private and then make use of SAS scheme which will put some kind of control and not allow blob to be accessed anonymously.
You can't hide or mask but there are some alternatives. You can make use Azure CDN or AFD on top of Azure Storage and then make call via that. This way the storage account will not be exposed directly.
With CDN, it provide an option of re-witing the rules as well so you can generate a URL along with SAS at the CDN level which will help controlling the security as well.
Let me know if there are any further queries/concerns, will be glad to assist.
Please do not forget to "Accept the answer” and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.