At the minimum you always want to give the other person your name. As long as you do that, you haven't made a horrible mistake. If you feel that you want to say more, I would recommend considering:
- Your body language
- How they were introduced to you
- Whether there are any connections/common ground
A large part of how we communicate is through body language and expression. No matter what you say, if your hold your shoulders in, head down, and speak softly, chances are that the person will feel you don't want to talk to them. Regardless of how short or simple your response is, try your best to smile, look at them, and stand up straight. This will make you seem more 'open' and easy to approach.
How they were introduced
In this case your manager introduced the person with:
- Their name
- Where they are from
- The project they are working on
So as a bare minimum you could say something like:
Nice to meet you Mr. X. My name is User from Planet Mars. I'm working on Project A.
Mirroring the information provided to you will rarely be a wrong choice. If you happen to be from the location of the office, you can give other relevant information of a similar nature, for instance.
Nice to meet you Mr. X. My name is User and I work for Mr. Manager. I'm working on Project A.
If you have any common ground, it usually makes people feel comfortable/makes you seem more friendly if you talk about that common ground. Here are some examples:
You've visited the UK Office Before
Nice to meet you Mr. X. My name is User, I'm working on Project A. I visited the UK office last year to work with Mr. Y, have you met him before?
You are working on the same project
Nice to meet you Mr. X. My name is User, and I'm also working on Project Z, creating widget B in team C. I look forward to working with you while you're here.
Your friend is working on the same project
Nice to meet you Mr. X. My name is User, and I'm working on Project A. My friend is working on project Z too, her name is Alice -- have you met her yet?
There are plenty of ways you may share some common ground. These are just examples, but the general idea is to bring up something that gives the other person the option of continuing the conversation with.