I want to give name for my daughter "Arshiya", Question: is there any element of Shrik by giving this Name to a child?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

We do not know any Islamic impediment that prevent naming a baby girl by the name you referred to in the question (Arshiya, or Arshiyyah).

Some earlier jurists were named Al-‘Arshi (which is the masculine name of ‘Arshiyyah), such as the Shaafi'i jurist ‘Umar ibn Muhammad ibn Yahya ibn ‘Uthmaan Al-‘Arshi .

Ibn Hajar wrote a biography about him in his book Ad-Durar Al-Kaaminah.

Nonetheless, there are many good names one can use instead of this name, such as the names of the daughters of the Prophet his wives, and many other good names of righteous women.

For more benefit, please refer to Fataawa 286006, 373321, and 200387.

Allah knows best.