Extended use of the Complement of direction and 把。 I was under the impression that you cannot say:


  *我把他的名字想不起來。


Because our book says you cannot apply 把 to 可能補語。
But now my fellow students pointed out that 想不起來 is no 可能補語, but rather 趨向補語的引申用法。

Does the same rule apply, or is the sentence correct? My grammar book says that 趨向補語 frequently acts as 可能補語 (for example: 自行車壞了，我騎不回去了！). It seems only natural, that the same restrictions should apply.

When I have 想不起來 on its own without 把，can I even unambiguously say, whether it is the negative of 可能補語 or 趨向補語？
You cannot apply 把 to a verb phrase with potential particle because 把 is a dispositive marker. A dispositive marker marks an object to be disposited of by a verb. For example: in (把)他趕走. the object(他) is being disposited of by the verb 趕走 (chase away). 

When a potential particles (得 or 不) is inserted between a verb and its resultive/ directional particle, that verb becomes a potential verb. For example:  趕走= chase away;  趕得走 = able to chase away.  It can no longer be applied to [dispositive marker + object] structure which requires an active verb at the end.

Example: in 我(趕走)他 , (趕走) is an action verb; in 我(趕得走)他, (趕得走)is a potential verb- You can, but you are not actively preforming the verb)

For the same reason, 我把他的名字(想起來- active verb) is correct, but  我把他的名字(想不/得起來- potential verb) is incorrect

To make '我把他的名字想起來' negative , you have to modify 把 with a negative marker like 沒 or 未 , for example: "我(沒)把他的名字想起來"


  When I have 想不起來 on its own without 把，can I even unambiguously say, whether it is the negative of 可能補語 or 趨向補語？


Without 把, there's no object to be disposited of,  '想起來' (active verb) or '想不起來/'想得起來 (potential verb) can be applied.

The sentence can be "我(想起)他的名字來" or, "我(想得起)他的名字來,  "我(想不起)他的名字來"- (you are not actively preforming the verb)