Word for a person who is "in charge"?

In the context of a department or realm of work, I would use manager, as in:

Is the manager of this department in today?

In the context of an individual I would probably use supervisor, although manager would work as well:

May I speak with your supervisor please?

If you are talking about a specific task rather than a department, you might use the phrase in charge like this:

Who is in charge of restocking the snack cupboard?

Lastly the verb head up can also be useful in contexts of projects or teams:

Who is heading up the backup team?
Who is heading up the security audit?

In earlier times you would use the word Manager

Can I speak to the manager?

Nowadays with so many titles and since you do not know the specific one that applies in that area (eg: Administrator, Supervisor, Boss etc) , it is getting popular to use "person in charge" as in the examples you have used.

I can think of two simple words: head and leader.

Examples:

• Who is the head [of the department] here?
• Do you know the department's leader?

I would use superior.

Can I speak to your superior?

It can work for anyone who is above someone else, even if it's not a managerial position.