Can you choose not to untap a creature you control during your untap step?

By default, untapping permanents during your untap step is mandatory, not a choice. Comprehensive Rule 502.3 states that the active player untaps all permanents they control during the untap step. There is no built-in option to simply leave a creature tapped if it would otherwise untap.

However, some cards specifically grant you the option to not untap a permanent. These cards use phrasing like 'you may untap [permanent]' or 'does not untap during your untap step.' When such an effect applies, untapping becomes optional or is explicitly suppressed. CR 502.4 clarifies that effects can modify what untaps during this step.

There are also cases where a permanent simply doesn't untap because an effect says it won't — for example, if an opponent's card says 'this creature doesn't untap during its controller's untap step.' In that case it's not a choice either; the card just stays tapped.

Concrete example: You control a Gloom Surgeon (a vanilla creature) and a Sword of Feast and Famine-equipped creature. After combat, both are tapped. During your untap step, you must untap the Gloom Surgeon — you cannot choose to leave it tapped. The Sword of Feast and Famine's ability let you untap all lands (optional phrasing), but the creature itself untaps automatically unless an effect says otherwise.

In summary: untapping is mandatory under normal rules (CR 502.3). Only a specific card effect granting optionality or preventing untapping changes this. You cannot simply choose to keep your own creature tapped out of preference.