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As the time goes, I find so many grammars in Japanese end with ～がある. For
example,

  * ～ことがある
  * ～必要がある
  * ～傾向がある
  * ～可能性がある

I know the ～がある means "there is" and they are so powerful. However, what I
don't quite understand is why Japanese says the following?

  * 私はアレックスだ。rather than 私はアレックスという名前がある。

  * この料理はおいしい。 rather than この料理はおいしい味がある。

  * プレゼントを買ってもらって、うれしい。 rather than プレゼントを買ってもらって、嬉しい感じがある。

  * 彼は態度が悪い。 rather than 彼は悪い態度がある。

Furthermore, are there alternatives for

  * experience
  * necessity 
  * tendency
  * probability

without using ～がある?
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question
grammar nuances possession
What is the basic underlying idea of ～がある?
~がある generally means 'there exists' or 'there is.'

To use your examples:

```

    ～事{こと}がある
    
```

~ has happened. _or_ ~ happens on occasion.

```

    ～必要{ひつよう}がある
    
```

There is a need to ~. _or_ It is necessary to ~.

```

    ～傾向{けいこう}がある
    
```

There is a tendency/propensity ~.

```

    ～可能性{かのうせい}がある
    
```

There is a chance/probability of ~.

**BONUS** Can we say, for example, 私は植芝{うえしば}という名前がある？

If you are saying your name is 植芝 you would say:

植芝と申します。どうぞ宜しくお願いします。
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answer
> why Japanese says the following?

This is simply because we don't always need the nuance of "there is" or "there
exists". This applies to all the four examples below.

Compare these more literal translations:

> 私はアレックスだ。 / I am Alex.
>
> 私はアレックスという名前がある。 / There is the name "Alex" of mine.; I have the name
> "Alex".

The latter sounds like the speaker is giving weight to his name rather than
himself. Indeed, this Japanese sentence could imply that the speaker is proud
of his name.

In fiction, we often see a character say 俺には○○という立派な名前がある after he is called
お前 or そこの etc.

* * *

> この料理はおいしい味がある。

This sounds unnatural, though おいしい味がする is fine. I'm not sure "This dish has a
good taste" is common in English but it's not in Japanese.

This is because we are not interested in the existence of tastes but how good
or bad it tastes.

* * *

> プレゼントを買ってもらって、嬉しい感じがある。

I actually sometimes say ～感じがある on Twitter, but it's not at all formal
writing. It sounds indirect.

* * *

> 彼は悪い態度がある。

We don't say this. As you mentioned, 態度が悪い is far better. Alternatively,
悪い態度が見られる is also OK. It has a little more objective sound.

* * *

> Furthermore, are there alternatives for
>
>   * experience
>   * necessity
>   * tendency
>   * probability
>

>
> without using ～がある?

**experience** : You can use 経験する (to experience), 以前（昔）～した (I did ～ before)
etc. but I think ～がある is common.

For example:

> オーストラリアへ旅行に行った **ことがある** 。 == 昔オーストラリアへの旅行を **経験した** 。

**necessity** : You have many options. 必要だ(na-adjective: necessary),
～しなければならない(have to), ～せざるを得ない(have no choice but to) etc.

> さらに議論する **必要がある** 。 == さらなる議論が **必要だ** 。 == さらに議論 **しなければならない** 。

**tendency** : Choose appropriate ones: 傾向が見られる(tendency is observed),
しがちだ(often do), よく～する(often do), ～タイプだ(slangy; mostly used for a person),
他と比べて～だ(more ... than others)

> 日本人は長時間働く **傾向がある** 。 == 日本人は **他と比べて** 長時間働く。
>
> 彼は感情が顔に出る **傾向がある** 。 == 彼は感情が顔に出る **タイプだ** 。

**probability** : There are variety of ways to mention probability. Care about
the level of probability. ～かもしれない (equal meaning to 可能性がある; not mentioning the
value of probability. less formal), ～可能性が考えられる, ～ないとも限らない, etc.

> 日本が優勝する **可能性がある** 。 == 日本が優勝する **かもしれない** 。

* * *

I noticed that noun + がある (where the noun is often 漢語) sounds more formal than
others. So you might have read many formal pieces of writing but not so many
informal or colloquial ones. If you turn your eyes to informal ones, you might
find various new expressions.
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answer
To go over the basics, as you already know:

  * `ある` means "to exist", "there is"
  * `X がある` means "there is a X"
  * `A (に)は B がある` means what in English "A have a B"

> **私はアレックスという名前がある。**

So this sentence means "I have a name Alex". When do you use it? I suppose
that when the phrase is uttered, whether you have any or a certain name is in
question. It's actually very natural if you say:

> 「外人」と呼ぶな。私はアレックスという名前がある。

But when you introduce yourself, i.e. what they want to know is your identity,
this response isn't a optimal phrasing. 私はアレックスだ "I'm Alex" would be more
suitable for such a situation (of course, in most occasions you'll have to
choose the polite form).

> **この料理はおいしい味がある。**

This one is unnatural not (mainly) because of ある but おいしい味. You just couldn't
say 味がおいしい because it'd mean "the taste tastes good".

> **プレゼントを買ってもらって、嬉しい感じがある。**

This one is mostly miswording, too. 感じ doesn't perfectly fit "feeling", but
closer to "what is felt from" or "impression". If you go:

> プレゼントを買ってもらって、嬉しい気持ちがある。

it will be at least natural. But the sentence still doesn't express your
happiness without reserve. It'll sound as if you had other complex emotions at
the same time, or were trying to distance yourself from your feeling. To
express your heart you can just use mental verb directly e.g. うれしい. If you use
those expressions every time I'd suspect you have serious autism or something.

> **彼は悪い態度がある。**

This may be the only real problem with the criteria of ある. I think the most of
times when you use "have bad attitude" in English, the "attitude" is merely a
resultative phenomenon that isn't construed as an entity deserved to "be" in
Japanese. You cannot say 態度がある in Japanese until an "attitude" can be actively
adopted, or conceptually separated from individual action takers. For example
(from Google):

> 男には好きな人の前で必ずとってしまう態度がある (generalized attitude)  
>  譲ろうとする態度があると、相手も譲ってくれるようになります (conscious attitude)

For the same reason, we don't say *いい／悪い姿勢がある but only 姿勢がいい／悪い "have
good/poor posture".

> _Furthermore, are there alternatives for ... without using ～がある?_

Not likely as long as you choose the noun forms. What you list above are all
appositive, which means, for example, `X 必要がある` and transposed `必要が X` don't
tell the same thing. Of course, you could reword them with equivalent
expressions:

  * ～必要がある → ～が必要だ・～しなければいけない／ならない／etc.
  * ～傾向がある → ～がちだ・～やすい
  * ～可能性がある → ～かもしれない・～となりうる

ことがある is already an idiom, I don't think there's another grammar to replace.
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answer