SUMIF formula explained

Here's my question.

In one column (A) I have names running down the page. In Column (B) I have numbers for those different names running down the page. In a completely different cell (G3) I need a formula that recognizes a specific name (lets say "Mark") in column (A) and then adds ONLY the numbers in Column (B) that pertain to "Mark" for a grand total in cell (G3).

There will be a thousand rows so this formula could save me hours.

Any help greatly appreciated

Thank you