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Please note that this is 4-phenylbutanoyl chloride:

4-phenylbutanoyl chloride

My guess was that another molecule of 4-phenylbutanoyl chloride would react with the phenyl, thus forming a structure like the one below:

My guess

But this molecule seems somewhat awkward, and I am unable to name it. Is my guess correct? If yes, what would be its name?

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My guess was that an other molecule of 4-phenylbutanoyl chloride would react with the phenyl [...]

Your guess is not that bad and it seems that you have identified the type of reaction.

Apparently, it is a special type of electrophilic aromatic substutution, known as the Friedel-Crafts acylation. In your guess, one molecule of the starting material would serve as the acylating agent (through the acyl chloride), while another is acylated at the phenyl.

What if you only had one molecule of the staring material? Can you imagine a similar reaction?

The alkyl chain of $\ce{CH2}$ that links the acyl chloride unit to the phenyl is flexible! There's no reason why the Friedel-Crafts acylation could not happen as an intramolecular reaction, where acylating agent and the attacked phenyl group are part of the same molecule.

What would the the outcome?

The intramolecular reaction would furnish tetralone. enter image description here

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