I want to say "museum curator". "museum" is "博物馆", while "curator" is "馆长".
So it should be "博物馆馆长".
However I heard someone say "博物馆长", ignoring the repeated word.
Is that a correct term? What's the difference?
You may ignore the repeated characters only if the last character of the first word can be omitted conventionally without changing its meaning.
For example, 北京市市长 can be shortened as 北京市长, because 北京 can already carry the meaning of 北京市 in this context. The 省, 市, 县 suffix is usually omitted when the length of the place name has more than one characters.
So, you could not name 沙县县长 as 沙县长, because 沙 doesn't sufficiently carry the meaning of 沙县. This rule may be applied to the case you've mentioned. People may think 国防部长 is acceptable while 央行长 sounds strange.
Generally, if the first word (even short form) is made up of one character in the name part, like 央行 (the name part is 央, the role part is 行), and second word starts with 行, it is not correct to reduce two 行-s to one.
If the first word (even short form) is made up of at least two characters in name part, like 国防部 (the name part is 国防, the role part is 部), and second word starts with 部, use one 部 or two are both acceptable. But finally, it is recommended using the full form, like 央行行长, 国防部部长, after all these are the exact right address.