As a new 2LT, how do I introduce myself to my troops?

I think you are overthinking this. Don't force introductions, just meet them in the course of events.

As soon as humanly possible, buy and read Small Unit Leadership by Col Dandridge Malone. It absolutely kills me that this was NOT written by a Marine. Read it once a month for a year. Once a quarter for another year, then once a year until you leave the Army.

I'm going to use USMC alphabet soup terms from 30 years ago, but will try to keep them plain English.

When you take over, there should already be a quarterly or monthly training plan in place, don't go about making a lot of changes, or "re-arranging the furniture" to show it is your platoon now. It is and you don't have to prove it to anyone. Talk to the Company CO and get his assessment of the Platoon, your Platoon Sergeant, Squad Leaders and Team Leaders. It may be tempting to talk to the Company XO or Company HQ SNCO's; don't without the CO's permission. They're his staff not yours. Also find out if there are problems with how the Plt interfaces with the Co HQ for support.

Then talk to your PltSgt get his assessment of the Squad Leaders and Team Leaders ask about superstars. Don't asks about turds, they'll ID themselves or maybe a clean slate will give them a chance to turnaround.

Read the Battalion and Company TEEP (Training and Exercise Plan) plans for as far out as they exist. See if the plt training plan supports the Battalion and Company TEEPs

Spend way more time observing and listening than talking or teaching. In my opinion the best platoon's were the ones where the leaders trained their immediate subordinates. So that no trainer is actually training more than 3-5 trainees. Too many LT's try to put their entire platoon through the advanced MOS course they just completed, with the LT as the primary instructor for everything. If they are sitting in a classroom or on bleachers and you are talking to the entire platoon, no matter what you think you are saying, they are hearing "Go to sleep."

You should be observing your subordinates train their trainees and quality checking, plus making sure it is within doctrine. If it's not get a good explanation why, find out if the variation is uniform to the platoon, company, and battalion. Confer with your plt sgt and your CO.

"Hi, I'm 2LT so and so..." Sir, in all reality, as long as you don't act like a condescending prick you will be okay, I promise. There are few things that are going to happen and they happen to ALL leaders (NCOs and Officers). First, you are not going to get everyone to like you. There will always be someone who doesn't. Second, you shouldn't care about having everyone like you because you aren't there o make friends; you are there to do a job. Lastly, you will be treated like a child by NCOs and this is for a good reason, unless you are prior service you don't know anything... Seriously, you know nothing... Learn from the NCOs and you will do just fine. They won't lead you down the wrong path. Good luck and have fun. Oh, and just a little extra advice: Do not call NCOs by their last name. They earned those stripes. If there is one thing that my peers and I hated it was being called by our last names by new LTs. Call them sergeant, respect goes both ways.

Hello I'm 2LT Miller, I will be your new PL... HUGE pause while eyeballing everyone individually. Then say something cool as shit like, " and if any of you woke up thinking you wanna start shit with me, think twice, because I woke up wishing a motherfucker would." Then just slowly walk away.

So how did it go, LT? Did you make it?

I model my command style on Capt Zapp Brannigan and CPT Herbert Sobel.

Seriously though, first impressions are important but don't overthink it. Your actions during your time as a PL will speak louder than words. Unless it is super memorable, with pyrotechnics and cheerleaders, they won't remember it anyway. What they will remember is how you lead.

depends on the unit , but irregardless of MOS they have been doing their job and have functioned without you. you are not the supreme savior . come in and observe. learn strengths and weaknesses and then offer advice..... chances are they tried whatever you think is high speed 3 LT's before. your PLT. Sgt can be your best friend

I got a big laugh out of this one.
When I was a young Corporal in 73, My new Captain introduced himself AFTER he busted our asses with a brutal PT period, followed by a hard 10 Km run through the hills of Fort Knox KY. We were in fairly good shape so only the profiles didn't finish. This was followed by another, but less-tiring set of exercises. Finishing with us, he sent us off to shower and breakfast.
At work call formation, he was smiling, joking and asking each soldier about his-self as he inspected each platoon. No one messed with him during his command tour - I'm still not sure if it was because he sincerely cared for us soldiers or because no one wanted to piss him off and find out he knew a really evil way to hurt us :D
Good Times and his command though hard has given those that were there in that cavalry troop bragging rights since.
Think about it but, "Choose Wisely." You have to do that type of thing using your strengths.

Attempt to have a platoon gathering in an informal place, but not with beer and pizza. The following is something to think upon: "I have met some of you, but have not taken the opportunity to address the entire platoon. I intend to coordinate closely with our platoon sergeant, Sergeant Smith, in all matters, just as he does with his squad leaders on matters of importance. Above all, remember that respect goes both ways and I will see that I will do my part in the deal. I simply ask to jointly make this platoon a step or two above where we are now. Thank you."

Sir, the best place start is your CO and 1SG. They can give you some insight. They will likely take the reigns of introducing you to the platoon sergeant. Then, I would strongly encourage follow his advice from there.

But remember keep it short and sweet. Those Soldiers don't care if you graduated from Westpoint or earned it online from American Military University and went to OCS.

Keep it under two minutes. Who are you? Do you have a Family? What are their names? Where are you from?

Be relatable and don't talk down to them. Make sure they know you're looking forward to growing as a Soldier with them. This is the first chance you get to earn their respect. Use it well.

Introduce yourself to your Platoon briefly, and then get to know each individually later. I just told them my name and my overall ethos - Do your job. Look out for each other. Keep me informed. No long speech of your past, just a general overview of your main requirements. Your actions will reinforce your words after that, provided you live up to your own ethos.