Asalamu Alaikum,

Your question is one that I had for many, many years and could not find a direct answer too. So, I hope this helps many sisters out there whether that are converts or not. The short answer to your question is black abayas are not a must.

You can absolutely wear any cultural style you feel comfortable in as long as it is fulfills the Islamic guidelines of hijab. Western style of clothing is not haram in and of itself. In fact, any cultural style can conform to hijab as long as it follows the following guidelines.

“Obligatory cover: males should cover at least from the navel to the knees. And women should cover the complete body except the face and the hands. Islamic clothes for both sexes should NOT be:

• So tight to the extent of detailing the figure.
• Transparent or see-through.
• So alluring that it is meant only to attract attention.
• Particular of the opposite sex.
• Resembling styles that identify — or are symbols of — other’s religions.” –Sahar El-Nadi

Also check out this link that discusses the same topic from a different cultural perspective. 

I hope this helps. May Allah make you successful in your efforts to draw nearer to Him by following His commands.