The most common term for an umbrella made out of plastic is simply called a "Plastic Umbrella".
Many times umbrellas can be made from this kind of material which is usually a flexible kind of plastic, or it could also be made out of other materials such as cloth or fabric.
If an umbrella is made of plastic, we call it a "plastic umbrella". A plastic umbrella is much more useful than umbrellas made from other materials when there is wet weather. A paper umbrella may protect us from the sun, but it does not keep us dry when it rains!
Umbrellas can be made from different things these include cloth/fabric etc
Vinyl is also called plastic, If you are talking about an umbrella made from plastic then it is called a 'plastic umbrella' you can also say a 'PVC umbrella'
PVC is a plastic polymer material
You have an umbrella made of plastic. If you wish to describe this item, just add the adjective 'plastic' to the noun 'umbrella'. To describe anything, just add an adjective to a noun - and then use an appropriate verb and subject to complete the sentence.
Eg. 'John is a perfect gentleman.'
(Subject) (verb) (article) (adjective) (noun)
プラスチック製の傘を説明したいなら、単純に名詞の 'umbrella'(傘)に形容詞の 'plastic'(プラスチック製の)を加えましょう。
何かを説明するときには、名詞に形容詞を加えます。そして、適切な動詞と主語を使って文を完成させます。
【例】
'John is a perfect gentleman.'(ジョンは完璧なジェントルマンです)
(主語)(動詞)(冠詞)(形容詞)(名詞)
There are not too many variations on this if you want to be specific about the material the umbrella is made from. Another word for vinyl is plastic. It is also the most common.