I am in the U.S. I joined this company 2 months ago (it's a large, global corp.), and now my boss says that my title is something else and not what I signed to in the offer letter. This "change" happened without informing me. I only found via the company's employee directory. Is this allowed? 

I understand responsibilities and roles can change, but I am fairly certain it is something both parties have to agree to. I requested that my boss and I have a discussion about this, and I cc'd his boss on this as well. 

My hope is to salvage things, and I don't want to jump ship so quickly. Any advice?

Edit to say: I checked the offer letter, and it does not have a clause about them being able to change the title at discretion.

Edit2: for context about the my job- it's within a business analysis unit that works on metrics of technology products. The title I agreed to had the word "manager" in it, and the one my boss is saying now doesn't. I expect this change to have an affect on my career development in the company.

Edit3: thanks for all the comments, all. My boss says I can use my previous title externally. I will do that, but I do feel blindsided that within the company I am not what I thought I was going to be when I joined. I am going to not care about that for now, and just focus on what I will be doing.