Looking at the screenshot you have attached, you are using the classic experience of Document Library. In classic experience, there doesn't exist default dynamic adjustable option to adjust any of the columns width in library/list views as well as in Quick Edit Datasheet view. You would have use code based solutions only to set the width of the required columns (Please see this link for one of way to set the width for your required column - https://techcommunity.microsoft.com/t5/sharepoint/customize-the-width-of-column-in-share-point/m-p/9...)
Would recommend you to select and make use of Modern Experience (New Experience) of the SharePoint Document Library which by default allows you to adjust the columns width and in fact you could set and persist the columns width by saving the view which will make those set columns width available to all users in modern experience. [With the assumption that there doesn't exist any customizations done in your current Document Library that are not supported in the Modern Experience].