Toot your own horn. To toot your own horn is to talk about your own achievements.
Give credit where credit is due. The speaker names the person who did the work.
Take credit for. A person who takes credit for something claims the work, sometimes work that someone else did.
Steal someone’s thunder. This means to take the attention that another person had earned.
A feather in your cap. This is an achievement that adds to your record.
The squeaky wheel gets the grease. The person who speaks up gets the attention.
Visibility. In office speech, visibility means being seen by the people who decide on promotions.
Humblebrag. This is a boast that is disguised as modesty.