In Salesforce SOQL, we use dot notation to get the parent record information. Similarly, we can do the same in the Lightning Web Component uiRecordApi.

Sample Lightning Web Component:

HTML:

<template>
    <div 
        class="slds-notify slds-notify_alert slds-alert_error" 
        role="alert">
        <h2>
            {accountName}
        </h2>
    </div>
</template>

JavaScript:

import { LightningElement, api, wire } from 'lwc';
import { getRecord, getFieldValue } from 'lightning/uiRecordApi';
import ACCOUNT_NAME from "@salesforce/schema/LiveChatTranscript.Contact.Account.Name";
import { ShowToastEvent } from 'lightning/platformShowToastEvent';

export default class AccountDetailsForChat extends LightningElement {

    accountName;
    @api recordId;

    @wire( getRecord, { 
        recordId: '$recordId', 
        fields: [ ACCOUNT_NAME ] 
    } )
    wiredRecord({ error, data }) {

        if ( error ) {

            console.log( 
                'Inside error block' 
            );
            let message = 'Unknown error';

            if ( Array.isArray( error.body ) ) {

                message = error.body.map(e => e.message).join(', ');

            } else if ( typeof error.body.message === 'string' ) {

                message = error.body.message;

            }

            this.dispatchEvent(
                new ShowToastEvent( {
                    title: 'Some error occurred',
                    message,
                    variant: 'error',
                } ),
            );

        } else if ( data ) {

            console.log(
                'Account Name Value is',
                getFieldValue( data, ACCOUNT_NAME )
            );
            this.accountName = getFieldValue( data, ACCOUNT_NAME );

        }

    }

}  

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>58.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordPage</target>
    </targets>
</LightningComponentBundle>

Output: