One example could be when you meet a person (Peter Parker) and remember only that his name starts with P or may Par.
An example of this could be a "hazy" or "vague" recollection. Assuming you're looking for a word that means to partially recall something.
Well, let me offer you not a word but an idiom: on the tip of (one's) tongue
According to the Free Dictionary
- If something such as a word, answer, or name is on the tip of your tongue, you know it and can almost remember
You can almost remember Peter's surname but not fully complete.
As pointed by @nnnnn, notice that it also applies when you can't remember any part of the word you're trying to think of, it's not specific to remembering part of the word.
In psychology/memory studies, this is called interference or rather a specific type of interference called retroactive, this is when later learning (this can be any information) hinders previously discovered or “learnt” material:
the tendency of later learning to hinder the memory of previously learned material.