If I good remember, the hotel was called the Grande Paradisio.
There are two problems here; one is word order, which actually wouldn't solve our problem.
It is, in fact, 'good'.
The speaker is trying to think what was the name of a particular hotel that they know - maybe they stayed there - and
they are basically commenting on how good their memory is of this name.
The correct phrase should be If I remember correctly (or rightly), the hotel was called the Grande Paradisio, or even If my memory serves me right, the hotel was called the Grande Paradisio.
And you probably shouldn't replace 'good' with 'well', because If I well remember would still sound unnatural. Evening chaging the word order won't help: If I remember well, the hotel was called Grande Paradisio, although if you say, for example, Julie from class 6? Oh, I remember her well or do you remember that Christmas when it snowed in 2000? No, I don't remember it well would sound perfectly natural. So the speaker might say: The Grande Paradisio hotel? I remember it well although this sounds a little on the formal side. I'd probably say The Grande Paradisio hotel? Oh yeah, I remember it/I remember it very well!
I understand that the above phrase is quite common among language students and I've had my own conversation students claiming they were never corrected on this.
Anyway, we as native speakers would understand what you were saying, and we'd probably understand 'If I well remember' being an acceptable mistake, but, really, don't say 'good remember' because, for sure, a native speaker will tell you that's wrong.
So hopefully you'll remember this well.