I am using iOS 11.2.6 on iphone8. While opening Safari, I am not getting any search engine options or icons.

You might check: Settings>Safari... and set its settings.

If you want to find details, I suggest that you read the "iPhone user manual for iOS 11" (section App>Safari).

You can find it here: Apple - Support - Manuals

Regards

Giulio

https://help.apple.com/iphone/11/?lang=en

If you want to search for something, type your search term into the box at the top and tap return.