Raising 3 BBs as UTG with AQo in a 8 players table?

Like most poker questions, it depends.

Is it the type of table where a 3bb raise is considered a limp and you are going to see a flop against a minimum of 4 opponents, out of position, with a hand that has high reverse implied odds? Then yes, it is probably -EV. Is it a table where a 3bb raise UTG will get you heads up against a weak tight player who will fold to any continuation bet unless they hit top pair? Then it is probably EV+.

It all depends upon the skill of the people you are playing against. Skill meaning calling frequency, post flop stickiness and trickiness.

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depends on the table. if you're playing a bunch of nits you don't want to raise too much else they'll fold out everything but hands better than yours. on the flip side, if you're playing a whale it might be +EV to open 10x the bb to get heads up with the whale. all about table dynamics

Against 7 opponents, AQo, a good hand, has a showdown equity of about 20%. So, in the very unlikely situation that all players call, the pot to be won will be 1.5+7*3 =22.5bb. Thus, you have pot odds of about 7 to 1, so you only need equity of about 12%, which you have.

Now to be more realistic. Through a simulation program I developed, I found that the probability at least one of 7 players has a pair or higher ace kicker than queen is 39%. AQ vs a pair is a slight underdog and AQ vs a higher kicker is a 70/30 underdog. So, if just one player calls with a pair or a better ace, say, on average, you are a 60/40 dog. (Actually, a weighted average should be used.)

Then, the lead bet EV of 3bb is: EV=0.61* 1.5 + 0.39*(0.40*4.5 - 0.60*3) = 0.92bb. Note that this is only a rough first cut evaluation using a showdown equity and assuming 1 possible caller. It ignores factors such as several callers, stack sizes, position, villain tendencies, tournament standing, folds and raises. One should adjust for these factors to the extent possible. Yet, I think doing such analysis is better than just a gut feel decision.

The fact that your simulation ignores position, stack sizes, and villain tendencies makes it's usefulness very limited no?

Seeing a flop with AQ out of position against an oppenent who will fold 99 on a J 10 3 board is very different than seeing a flop out of position against opponents who are much more willing to pay to peel one more card.