What is the name of the ambiguity in the phrase "I want to visit clubs with attractive women"?

Your sentence contains an example of ambiguity resulting from a misrelated construction. The Oxford Dictionary of English Grammar defines misrelated as follows:

Not attached grammatically to the word or phrase intended by the meaning, either joined to the wrong word or phrase, or completely unattached.

Although terms such as misrelated, dangling, hanging, unattached, etc. are most commonly applied to participles, verbless phrases can also be misrelated.

The offending misrelation in your sentence is not a participle but a prepositional phrase.

I think this is called Amphiboly. The first example I ever read was the phrase "half baked chicken".

Attachment ambiguity. The prepositional phrase "with attractive women" must be an adjunct of something, but of what? There are two plausible possibilities ("visit" and "clubs"), and that produces the ambiguity.

The sentence is grammatical, and can be (grammatically) parsed in two ways to produce the two alternative meanings.

A dangling modifier is different. We say there is a dangling modifier when the sentence cannot be grammatically parsed to yield the intended meaning. (It might or might not be possible to parse it to yield some other meaning. If there is such a meaning, it might be an absurd one.) Wikipedia's article gives an example "At the age of eight, my family finally bought a dog". Was the family at the age of eight? That is semantically nonsense. If the intended meaning is that the narrator was eight, then the sentence cannot be parsed to yield that meaning.

For the headline "Scientists discover emperor penguin colony in Antarctica using satellite images", refer to this section of A Comprehensive Grammar of the English Language (CoGEL):

(CoGEL § 15;59) Unattached nonfinite and verbless clauses

It is considered to be an error when the understood subject of the clause is not identifiable with the subject of the matrix clause, and perhaps does not appear in the sentence at all:

• ?Driving to Chicago that night, a sudden thought struck me. [1]
• ?Since leaving her, life has seemed pointless. [2]
• ?Walking down the boardwalk, a tall building came into view. [3]

In these examples the implied subject of the clauses is presumably I, but I does not occur as the subject of the matrix clauses. If we wish to keep the nonfinite clauses as they are, we rephrase the matrix clauses to introduce I as subject; for example :

• Driving to Chicago that night, I was struck by a sudden thought. [1a]
• Since leaving her, I have felt that life seemed pointless. [2a]
• Walking down the boardwalk, I saw a tall building. [3a]

This is a case of unattached nonfinite clause. No particular name is given in this grammar to the ambiguity it might give rise to; in most cases it is nonsense.

Addition

(CoGEL § 15.59)

As with [1-3], we can interpret correctly the implied subject in these sentences, but these unattached clauses are frowned upon. Such clauses are totally unacceptable if the sentence provides no means for identifying the implied subject:

• *Reading the evening paper, a dog started barking.
• *Using these techniques, a wheel fell off.
• *A result of the rise in prices, our economy is suffering.

Sometimes the error suggests an absurd interpretation:

• *Opening the cupboard, a skeleton fell out.
• *Grilled on charcoal, everyone enjoyed the fish they caught.
• *Having eaten our lunch, the steamboat departed.