私は 二 猫を います。 猫は 一 なまえ シャドち。 猫 二 なまえ ランジち。

I'm attempting to say, "I have two cats. cat one is named Shadow. Cat two is
named randy."
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grammar
Is this sentence correct. (Beginner sentence.)
Your translation is somewhat close, but some there are some errors. You are
going to want to use counters in this sentence.

"I have two cats" will use the counter for animals (hiki/piki). You'll want to
study counters more closely if you want to understand their meaning.

The second part of your sentence needs a little work. You're on the right
track, but lets see if we can work out some kinks.

I'm going to take some liberty and change the sentence above slightly so that
it sounds more natural. The translation and change are below:

```

    I have two cats.  Their names are Shadow and Randy.
    私は猫｛ねこ｝が二匹｛にひき｝います。名前｛なまえ｝はシャドーとランディです。
    
```

Here's how I would translate the sentence as you originally had it with only a
subtle change:

```

    I have two cats.  One is named Shadow.  The other is named Randy.
     私は猫｛ねこ｝が二匹｛にひき｝います。一匹｛いっぴき｝の名前｛なまえ｝はシャドーです。もう一匹｛いっぴき｝はランディです。
    
```

I hope it helps.
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Great attempt, but not quite. There are a few things wrong here.

First, to say you "have" something (that is a living being), you use THING
**が** います, not **を**.

Secondly, you need to use counter words ([助数詞]{じょ・すう・し}) which presumably you
haven't learned yet. To form them, you use `number + <counter word>`. For cats
and other small creatures (except for rabbits), the counter word is 〜[匹]{ひき}.
So in this case, you would say 二匹. Now to combine that with the "have" part,
you insert the counter before います. So you'd get

> 私は猫が二匹います。

Counters are a whole other area of study by themselves that I'm not going to
dig into here. They're not difficult, but it takes some practice to learn what
counters there are and what situation to use them in (for example, see [my
question about counting video
clips](https://japanese.stackexchange.com/q/9714/78)).

(Also, it's maybe a little more natural to say 私 **に** or 私 **には**. See [が and
に interchangeability and difference in
meaning](https://japanese.stackexchange.com/q/4440/78) for more about this).

Lastly, when using ordinals (i.e., 1st, 2nd, 3rd, ...) with counters, you use
the suffix 〜[目]{め}. So "first cat" is 一匹目, "second cat" is 二匹目, and so on.
However, this puts focus on the actual order, and since you're not really
ordering them, I'd suggest 一匹〜もう一匹 ("the first one 〜 the other one") as in
@ajsmart's answer. Also, your word order in the second sentence is a little
off and missing a few particles.

So your sentence would end up looking like

> 私は猫が二匹います。一匹目の名前はシャドです。二匹目の名前はランジです。

or

> 私は猫が二匹います。一匹の名前はシャドです。もうー匹はランジです。 (you could safely omit の名前 for the second
> one)
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> I have two cats. Cat one is named Shadow. Cat two is named randy.

家｛うち｝には猫｛ねこ｝が二匹｛にひき｝います or 私｛わたし｝は猫｛ねこ｝を二匹｛にひき｝飼｛か｝っています。名前｛なまえ｝はシャドーとランディーです。

As for _I have two cats_ , literally or logically 私は猫が二匹います could be said as
the translation of "I have two cats", but we don't say like that. But, 私
**には** 猫が二匹います could be said anyway.

And as for *Cat one is named Shadow. Cat two is named randy.", I agree with
ajsmart's answer that " _Their names are Shadow and Randy_ " is more natural.
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