We know Shiva is the Lord. But it is not clear what is meant by Shivaaya ?
My question is : What is the meaning of Shivaaya ?
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शिवाय (Śivāya) is 4th Vibhakti of शिव (Shiva). 4th Vibhakti means to/for whom.
So the meaning of Śivāya would be to/for Shiva.
Example: ॐ नमः शिवाय (Om Namah Shivaya): Om salutations to Lord Shiva!
Below are the basic details on 8 Vibhaktis:
The below lines of Ram Raksha Stotra have all the Vibhaktis in order:
रामो राजमणिः सदा विजयते रामं रमेशं भजे।
रामेण अभिहता निशाचरचमू रामाय तस्मै नमः।
रामात् नास्ति परायणं परतरं रामस्य दासोस्म्यहम्।
रामे चित्तलयः सदा भवतु मे भो राम! मामुद्धर।।३७॥
I worship Rama whose jewel (among kings) who always wins and who is lord of Lakshmi (goddess of wealth)। Through whom the hordes of demons who move at night have been destroyed, I salut that Rama [my salutations to that Rama]।
There is no place of surrender greater than Rama, (and thus) I am servant of Rama।
My mind is totally absorbed in Rama. O Rama, please lift me up (from lower to higher self)॥37॥
Shivay and Shivaya
We have a lot of meanings from Shiva (sanskrit शिव, IAST: Śiva) in the Vedas, but I will write about the etymology.
The teacher Bal Gangadhar Tilak in 1903 wrote the book "The Arctic Home in the Vedas" (the link to full english book in PDF). In it, he argued that the Vedas could only have been composed in the Arctics, and the Aryans (slavic folks) brought them south after the onset of the last ice age.
Šiwa, Živa, also Živena, Żiwia, Siva, Sieba, is the slavic goddess of life and fertility. She is worshiped throughout what is now Poland, the Czech Republic, Slovakia, and Germany (and especially the Elbe (Labe) river valley), before Christianity expanded into the area. Her name means "living, being, existing".
A large and dark main-belt asteroid "140 Siwa" (ˈʃiːwə) was discovered 1874 and named after Šiwa, the Slavic god.
In India the name Shiva is spoken from a lot of people like Siwa too.
When we would like to translate the word Zhiva (Šiwa / Živa) from slavic language into english then we have this meanings:
I think Shivay and Shivaya are the forms of russian words Zhivoy (rus. Живой) and Zhivaya (rus. Живая). We can understand the meaning only if we go to russian language. Zhivoy (rus. Живой) is in english "one men, who lives". And Zhivaya (rus. Живая) is in english "one woman, who lives".
This is my knowlege. And I hope it can help someone.
Hare Hare Mahadev! Ohm Namah Shivaya!
Concept of god Ardhanaareeswara - half men and half woman of god Shiva.
The half-man half-woman Ardhanareeswar represents the union of Shiva and Shakti, the basic tenets of creation, the unchanging Consciousness and Drive that gives motility.
சிவாய என்ற அச்சரம் சிவம் இருக்கும் அச்சரம் உபாயம் என்று நம்புவோருக்கு உண்மையான அச்சரம் - சித்தர் சிவவாக்கியர் பாடல்
This is Siddhar Sivavakkiyar song about true nature of soul = which is Shiva.
"The soul is running it's life in the body in the sound vibration of Si va ya
And this vibration works only for truly surrendered souls to the supreme"
Si va ya here refers to the sound in which your soul is living in the body. Also out of five elements of nature, the fire, air, and space energy's Sound vibration are - SI VA YA (not Shivay). The more you utter the mantra SI VA YA - it directly connects you to spiritual realm of vibrations.
That's why even avvaiyar also said "Those who think of SI VA YA without any deviation, for them no harm is done"