Alaikumassalam wa rahmatullah,
Ashriq (spelled as عشرق in Arabic) is the Arabic name for the plant known as Senna in English, which has many medicinal uses and has yellow flowers. In Arabic it is also called as-Sinaa Makki. You can use it as a name if you like it. It is a non-Quranic word. It seems to be mostly used for boys.
Ashriq (spelled as أَشْرِقْ) is a command to the sun to rise. In other words, if God said to the sun, "Ashriq!", the sun would come up. I haven't seen this meaning used as a name.
Ashriq seems to be mostly a Malaysian name and it is possible that it has another meaning in their language, possible related to the concepts of "east" or "sunrise".