Your familiar is still your familiar.
Find Familiar says:
Your familiar acts independently of you, but it always obeys your commands.
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar’s eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has. During this time, you are deaf and blind with regard to your own senses.
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons. Alternatively, you can dismiss it forever. As an action while it is temporarily dismissed, you can cause it to reappear in any unoccupied space within 30 feet of you.
None of these requires you to be smart or humanoid or even to have an unchanging body. If your race is changeling or verdan, you don’t suddenly lose your familiar when you transform. Because the familiar has a magical and a telepathic connection to you, it will still recognize and obey you.
Also remember that the familiar is not a beast; according to the spell, it’s a celestial, fey, or fiend spirit that takes an animal form. As such, it likely has a greater comfort with magical effects than you’d expect from a typical beast.
You might choose to role-play that your familiar is momentarily confused the first time you change into a particular form, but no game mechanic requires this. As an analogy, consider how a dog behaves when reunited with its human after a long separation. They may display an initial hesitance, but as soon as the dog catches the person’s scent, there’s instant recognition and acceptance.
You’re dumber than you were.
Although your familiar still functions the same, you do not. As you quoted from Polymorph:
The target’s game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.
In the case of the T. Rex, your Intelligence score is reduced to 2. To better understand what this means, it’s helpful to consider that number in reference to the scores of other common beasts.
INT = 1
INT = 2
INT = 3
So, as a T. Rex, you’re not effectively brainless like an insect, but you’re also not as smart as a dog. This will affect your communication, but it may not be as limiting as you might think.
Being dumb probably doesn’t limit your communication with your familiar.
It’s important to note that the Intelligence scores of Find Familiar‘s creatures are all between 1 and 3. Your owl shares the T. Rex’s 2, so you and it are now matching in intelligence.
You can no longer formulate complex thoughts, but your familiar wouldn’t have understood those anyway. You can still send telepathic commands, and although they’re likely not structured as language, they’ll still be as effective as necessary. For example:
- Come Here
- Go There
- Fetch That
- Stand Watch (i.e. remain alert and warn if there’s danger)
- Distract that Creature (e.g. fly into its face)
- Find “Timmy” (a party member or other creature known to the familiar)
- Search for Goblins
Communication with your party members is limited, but possible.
Like a horse or bear, the T. Rex will be able to use body language and simple sounds to communicate with party members in a limited fashion. Typical messages might be:
- I Acknowledge You (a huff)
- Follow Me (taking a few steps and then looking back at the person)
- I’m Angry, Excited, or Proud (a roar)
- Leave Me Alone (an incomplete attack, like a snapping of teeth)
- Thank You (a gentle nuzzle)
The giant ape you mentioned offers more interesting options. With an Intelligence Score of 7, it may well be smarter than any members of your party for whom Intelligence wasn’t prioritized during character creation! In this case, communication through more complex sounds, body language, and gestures would be feasible.
In fact, because some real-world chimps and gorillas have been able to learn rudimentary (and somewhat clumsy) sign language, you might take the time to develop a small set of useful signs to use with your party.
Don’t forget that you can’t cast spells.
One way your being polymorphed does limit your familiar’s function is related to their delivery of touch spells. Polymorph removes all of your spellcasting ability:
The creature is limited in the actions it can perform by the nature of its new form, and it can’t speak, cast spells, or take any other action that requires hands or speech.
The familiar would still be able to deliver any spells you sent its way, but your spellcasting has been disabled.
(Side Note: Some might argue that the wording here is ambiguous, and if your spells didn’t need somatic or verbal components — such as when using Subtle Spell metamagic — they would require neither hands nor speech, so you could still cast them when polymorphed. This interpretation is discussed here and here.)