Hi Nakmuay
First, this is probably more appropriate in the Trademark Forum. I'm guessing hat when you say "patented JJ over the moon", you really meant adopted a trademark (or Registered a Treademark) for 'JJ over the moon'
Trademark rights are created by used. The first to use a mark in commerce generally has senior rights to the mark. Before using mark however, you should have a trademark search and opinion performed, where your proposed mark is searched and an opinion regarding clearance is given by a qualified Trademark Attorney.
Trademarks are about protecting a consumer from being confused/misled into buying one companies product when the consumer believes that they are purchasing another company's product. If there is no likelihood of confusion (LOC) between the mark that you are adopting, and existing marks, than you would have no problem in adopting a mark.
There are several factors used in determining whether a LOC exists between your proposed mark, and existing ones. One factor is whether the marks are similar in appearance or sound. 'Hurshey' on a candybar would be confusing to a consumer to the Hershy brand candy bars. The closer the look or sound, on similar or related goods/services, the more likely confusion would exist. Another factor is the goods/services where the marks are being used. If one company uses the marks in the airline industry and another uses the mark in plumbing, then there is less chance a consumer would be cpnfused in thinking the companies or their products/services are related. Thus, you can have Delta faucets existing with Delta Airlines. However, if you had Delta jet engines you would have a problem. There are several other factors that are considered.
First this is NOT legal advice. A LOC determination is often a difficult determination, especially with so few facts. I'll assume that the goods/services between the product/service you wish to use the mark are similar to the company currenty using the mark.are related/similar. To me, assuming that the phrase 'over the moon' is not a common mark used in your industry, or a common component/part of a mark used in your industry, then you would seem to have a problem. Even though the marks are not completely identical (which is not needed to find confusion anyways), it seems that the phrase 'over the moon' is fairly dominant part of the mark (i.e., it would seem to be a phrase that would stick out in a consumers memory when recalling a brand). Thus, even if you use a different word before 'over the moon' as your mark, a person may still be confused into thinking that your product is somehow related to that product that they saw the TV commercial about 3 weeks ago, of the one that their friend told them about last week. However, if you are using the phrase in a completly different industry, and no one in that industry uses a similar phrase, you may be ok.
This question also presumes the question applies to trademark issues in the United States, as each country has its own standards and laws regarding whether a mark may be adopted for use.
Good luck. Again, the analysis really does involve other factors than discussed here, so please seek qualified advice before adopting a mark...