B. There could be a question as to who owns the name between two, or more, different groups who all perform under the same name. The actual ownership is usually decided by which artist performed under (i.e., used) the name first. However, there is a legal term called "secondary meaning" which could override first use. A secondary meaning is when the public identifies a name with a particular artist. The Rolling Stones are a good example. There is no question as to who this name refers to. It could be that another act using the name the Rolling Stones was around first, but the public identification is with the famous group. If the artist is just starting out and finds itself in a situation where there is a rival claim to the name, it is probably better to change the name early on to avoid legal hassles.
C. There could be a question as to who owns the name between the members of a group. This becomes a problem if a member leaves or the group breaks up. It is advisable for the group to enter into a partnership agreement, or form a corporation, so that this issue is dealt with in advance.
An artist should also be wary of any record label that attempts in the contract to have ownership rights in the name transferred to the label. The artist must refuse this request because it is unfair for the label to benefit from owning a name that the artist created and developed.
In conclusion, a name is very important and great care should be taken in selecting it, protecting it and clarifying ownership in it.
Ben McLane Esq