Step 1: Approach it from the truth table rather than the circuit diagram.
Instead of tracing every gate in the circuit, it helps to write out the output for all four combinations of two inputs $A$ and $B$, and see which standard gate's truth table it matches.
Step 2: Recall the distinguishing truth table pattern for each candidate gate.
An OR gate outputs high whenever either input is high. A NAND gate outputs low only when both inputs are high. A NOR gate outputs high only when both inputs are low. None of these three give a high output specifically and only when the two inputs disagree with each other.
Step 3: Match the circuit's actual behaviour.
The circuit shown produces a high output precisely when its two inputs differ, that is $0,1$ or $1,0$, and a low output when they are the same, that is $0,0$ or $1,1$. This "output high only when inputs disagree" behaviour is the defining signature of the Exclusive OR function, $Y = A\overline{B} + \overline{A}B$.
\[ \boxed{\text{EX-OR}} \]