What is the active form of
‘I love being given presents’?
I came up with ‘I love people giving me present’. But then I can’t change this into a passive.
I think the sentence you're looking for is
I love receiving presents.
Receiving is the active form of the passive being given.
I think you're right, but passivizing "people giving me presents" into "being given presents" requires a rather abstract analysis. The "-ing" is part of the Poss-ing complementizer, which is there because the sentence "people give me presents" has to be converted to a NP so that it can serve as object of "love".
The "my" which is expected for the subject of the passivized "give me" once the complementizer Poss-ing is applied is deleted because of the antecedent "I" which is subject of "love".
The "people" is lost because an unspecified passive agent is optional.
And there you have it.