11. He is also Sakala as He has an embodied form. He is both Sakala and Niṣkala. It is in his Niṣkala aspect that the Liṅga[1] is appropriate.
12-13. In the Sakala aspect the worship of his embodied form is appropriate. Since He has the Sakala and Niṣkala aspects He is worshipped both in the phallic and in the embodied form by the people and is called the highest Brahman.
20-24. O sinless one, since you are pious I shall tell you what Śiva Himself has said. Since Śiva has the bodiless aspect in virtue of His being the supreme Brahman, the Niṣkala liṅga, in conformity with the Vedic implication, is used only in His worship. Since He has an embodied form as well, His embodied form is also worshipped and accepted by all people.
Source : Shiv Purana Section 1 Vidyeswara Samhita ch 5
As per Skanda Puran, Linga represents Shiva and Shakti. Linga is said to possess all Gunas and Prakriti. That’s why Mahadeva is worshipped in the form of a Linga.
Vyāsa explained:
6. Listen, O dear one. I shall tell it. It was formerly explained by Nandī to Agastya who asked about it. O Śuka, everything was heard by him.
7. Know that the Great Ātman is devoid of Guṇas but it is in the form of Liṅga. Similarly Satī, the greatest and eternal Śakti, should also be known as devoid of Guṇas.
8. It is by her that this ultimately perishable universe consisting of mobile and immobile beings and evolved out of the three Guṇas, has been created.
9. The Ātman alone, the greatest unsullied Lord in the form of Liṅga (is eternal). Those three Guṇas got merged into it (the Supreme Ātman) along with Prakṛti.
10. It was hence called formerly Liṅga because of Layana (‘merging’). Even the Parā Śakti gots merged into the Liṅga. What of others?
11. At the instance of Rudra, the Guṇas whereby mobile and immobile beings are bound, become merged, O highly fortunate one. Hence one should worship Liṅga.
12. Know, O excellent Brāhmaṇas, that Liṅga is devoid of Guṇas. It is on account of the merging of the Guṇas that the Liṅga is glorified.
13. Śaṅkara is described by learned men as the bestower of happiness. He is called Sarva, O Brāhmaṇas, as he is indeed the support of all.
14-15. O Brāhmaṇas, he is called Śaṃbhu because he is one from whom auspiciousness originates. Thus all the names of the great Ātman are meaningful. The entire universe is enveloped by that Śaṃbhu, Parameṣṭhin (the Supreme God).
Source : Skanda Purana Maheshwara Khanda Kedara Khanda ch 20
As per Linga Purana worshipping Linga is highly auspicious as it is equivalent to worshipping all Gods including Tridevs.
May the questions of the sages stop. The whole world is identical with the Linga. Everything is found on the Linga. Hence, one shall eschew everything, install the Linga and worship it.
All the deities like Brahma, śiva, Earth, Lakshmi, dhṛti, smṛti, prajñā, durgā, śacī, Rudra, Vasu, Skanda, viśākha, śākha, naigameśa, dikapalakās(guardians of the directions), the planets, gaṇās, nandī, Ganapati, pitṛ gaṇās, ṛṣis , kubera, āditya, sāṃkhya, aśvinīkumārās- the best of the physicians, viśvadevās, sādhyās , paśus, birds and animals, besides all the mobile and immobiles, starting from Brahma are established in the linga. Therefore, leaving aside everything, linga should be consecrated. After consecrating it with all the efforts, incase, one adores the shivalinga, then he gets adorable by all.
Source : Linga Purana part 2 ch 46
Next chapter further says :
Lord Brahma resides at the root, Lord Vishnu in the middle. The lord of all unborn Pasupati in the form of Rudra resides at the top.
Source : Linga Purana part 2 ch 47
As per Linga Purana, Linga represents both Shiva and Shakti.
The Devotee shall clean Linga along with the pedestal and then devoutly install it. The pedestal of the Linga is Godess Uma and the Linga is Maheswara himself.
Source : Linga Purana part 2 ch 47