We can map through the departments array, and add a models property that equals the models array, but filtered only to the ones that contain a matching department id.

const departments = [
  { id: "1", name: "department1" },
  { id: "2", name: "department2" },
];

const models = [
  {
    id: "23",
    name: "model1",
    departments: [{ id: "1", name: "department1" }],
  },
  {
    id: "54",
    name: "model2",
    departments: [
      { id: "1", name: "department1" },
      { id: "2", name: "department2" },
    ],
  },
];

const getDepartmentsWithModels = () => {
  return departments.map((department) => {
    return {
      ...department,
      models: models.filter((model) => {
        const modelDepartmentIds = model.departments.map(({ id }) => id);
        return modelDepartmentIds.includes(department.id);
      }),
    };
  });
};

console.log(getDepartmentsWithModels());
// [ { id: '1', name: 'department1', models: [ [Object], [Object] ] },
//  { id: '2', name: 'department2', models: [ [Object] ] } ]```

There are two solutions.

Using Array.reduce() --> returns an object where the key is department name and value is an array of the names of matching models:

let data1 = models.reduce((res, curr) => {
    curr.departments.forEach(dep => {
        if (!res[dep.name]) {
            res[dep.name] = [curr.name]
        } else {
            if (!res[dep.name].includes(curr.name)) {
               res[dep.name].push(curr.name); 
            } 
        }
    })
    return res;
}, {});

 

Using map and filter --> returns an array of kind: [{department: [names of the models]},...]

let data2 = department.map(dep => {
    let matchingModels = models.filter(model => {
        return model.departments.filter(modDep => {
            return modDep.name === dep.name;
        }).length > 0;
    }).map(mod => {
         return mod.name;
    });

    return {
        department: dep.name,
        models: matchingModels
    }
});

I've built some code, which iterates over the departments. For each department it iterates the models and for each model it checks if the department is within the model departments.

const department =
[
    { id: '1', name: 'department1' },
    { id: '2', name: 'department2' }
]

const models =
[
    { 
        id: '23', 
        name: 'model1',
        departments: [{ id: '1', name: 'department1' }] 
    },
    { 
        id: '54',
        name: 'model2',
        departments: [{ id: '1', name: 'department1' },{ id: '2', name: 'department2' }]
    }
]

department.forEach( dep => {
    console.log(`Department: ${dep.name}`)
    models.forEach(model => {
        if (model.departments.find(modelDep => dep.id===modelDep.id)) {
            console.log(`  Model: ${model.name}`) 
        }
    })
})

If you could change your data objects, then your code could be much smoother.

I've changed your data objects slightly by just reducing the departments in a model to be an array of department id's. This code iterates over the departments. For each department it filters the models and iterates over the filtered models to output them to the console. This is lesser code and provides much better performance.

const department =
[
    { id: '1', name: 'department1' },
    { id: '2', name: 'department2' }
]

const models =
[
    { 
        id: '23', 
        name: 'model1',
        departments: ['1'] 
    },
    { 
        id: '54',
        name: 'model2',
        departments: ['1', '2']
    }
]

department.forEach( dep => {
    console.log(`Department: ${dep.name}`)
    models.filter(model => model.departments.includes(dep.id)).forEach(model => {
        console.log(`  Model: ${model.name}`)
    })
})