If you're playing on PC, it depends on which version you are using. For Java Win/Mac/Linux): no; Each named player needs a seperate login as your license is tied to your login/Microsoft Account. If the same user tries to connect to the same server, the previous connection will get kicked (Source: Have multiple accounts).
However, for Bedrock (Windows Store) edition, yes; you can install the game in multiple places using a single purchased license like with the app store (see below), but when you launch the game, each user needs to have their own separate Microsoft account. Otherwise a user conflict happens like in Java and the previous connection is kicked. Unlike Java Edition, accounts used to log into the game (seperate to the one downloading/installing it) do not need to own the game.*
If you're playing on mobile (Android + iOS), then yes; You can install the app on multiple devices having purchased it once by reusing the same Google Account/Apple ID, unless they're both on different platforms, then you'll need a copy per platform. Each person just needs their own individual Xbox Account and device (you can't split screen).
If you're playing on console (Nintendo Switch, PlayStation, Xbox, etc.) then no, you'll need a cartridge/license/account AND console per player, unless playing split-screen.
*Entitlements and subscriptions such as DLC (Marketplace) and Realms are per-account, though the account that installed the app is usally the payment instrument (who gets charged), especially for the case of Android/iOS and carry along with you regardless of whether you're playing on the Windows/Mobile/Console versions of Bedrock; just log into the same user (not the one used to download the app) account.