Correct spelling for the English word "stiled" is [stˈa͡ɪld], [stˈaɪld], [s_t_ˈaɪ_l_d] (IPA phonetic alphabet).
The word "stiled" is the past tense and past participle of the verb "style". The etymology of "style" can be traced back to Middle English, Old French, and Latin.
In Middle English, around the 13th century, the verb "style" (spelled as "stilen") meant "to designate with a title" or "to call by a specified name". It came from Old French "estile" which had a similar meaning of "to designate" or "to designate by a title".
Old French "estile" itself was derived from Latin "stīlus", which referred to a pointed instrument used for writing on wax tablets. Over time, "stīlus" came to be associated with writing in general, and eventually, its meaning expanded to include the manner or way of writing, speaking, or behaving in general.