Can I notify multiple users without specifying their names while creating the alert?

Yes. OpsGenie web API allows specifying the name of a "group" in the recipients field. Just create a "group", add users to the group, and put the group name into the recipients field

Example:

With this configuration, each member of the group would be notified as soon as the alert is created, according to the user's notification preferences. Using groups as the recipient instead of individual users may be preferred since modifying group membership is typically easier than modifying various integration scripts, email rules, etc. and can be done in a single place.