Can a finite automaton have more than one regular expression?
There are multiple ways of writing the same expression, then I guess yes, it can be represented by many expressions.

For example, look at this DFA (with the initial state being final)

--&gt;(a)________
    ^         |
    |         |
    |         V
    '--------(b)


the regular expression for it can take infinite forms, such as

$(ab)^*\;$ or $\;(ab)^*(ab)^*\;$ or $\;(ab)^*(ab)^*(ab)^*\;$ ...

If you consider different forms of the same expression, then it can be represented by lots of regexs, otherwise is just 1.