Mixing tenses in past tense fiction

In past tense works (novels, etc.) is there a place for some present tense verbs, such as "think" or "know" or "was."

Example: I turned to leave, and he didn't try to stop me. I think I surprised him. I know I surprised myself.

This sounds much more natural to me than "I thought I surprised him." Is there a word for this? A rule? Would you rephrase it? If so, how? Thank you.

This sounds much more natural to me than "I thought I surprised him."

Both have their place, and mean different things.

If the narrating perspective considers after the story (whether from an indistinct "now" of the storytelling, or from a particular framing time frame) that they had surprised "him", then this would be more appropriate.

If the narrating character thought then that they had surprised, then "I thought I surprised him" might be more appropriate. (The mixture of simple past and past perfect, "I thought I had surprised him" is different again, and also has its place).

Is there a word for this?

It's generally just called "mixing tenses" or "switching tenses".

It's important to note that while more basic instruction (whether to younger students, or to students of English as a second language) is not to mix tenses, this is in the category of "lies to children": Not only can one mix tenses in a great variety of ways, but one should mix tenses. The difference is between slipping from one tense into another (as perhaps might happen with a novice speaker more familiar with the present tense forms) and switching because it is appropriate to do so.

In your example of "I think I surprised him" is appropriate if present tense is appropriate for the thinking and past tense appropriate for the surprising, and not otherwise.

Really the rule is "always use a tense appropriate for what you want to express". Mixing tenses when one shouldn't is an easy way to break this rule for the most novice of English writers and speakers, but not mixing them when one should is another form of the same problem.

The mixed tenses are actually correct in this case:

I turned to leave, and he didn't try to stop me.
This is a complete action that happened in the past.

I think I surprised him. I know I surprised myself.
This is in the present because you continue to think that you surprised him, you continue to know that you surprised yourself.