As of February 24, 2016, no live official trademarks were found on USPTO.gov for the exact term
MonkeyBucket.com and MonkeyBuckets.com are long tail brandables, containing two strong dictionary words: Monkey and Bucket. and the plural Buckets.
Monkey seems to be a popular brandable dictionary word for whimsical sites and businesses. For example, we can see the singular for a funny website for children and the plural for a bar or restaurant.
Both names elicit a smile or chuckle.
Domains sold separately.
* * * * *