Are you referring to the label that comes with the textbox when you drag the field name over from the "Available Fields" window?

Access will always create a label for textboxes with the caption the same as the field name unless you turn that off in the control settings.

If you want to keep the label but be able to move it without moving the text box, you can grab the little square "handle" at the top left corner of the control. First click the label to select it, then the little box will show in the top left. Click and drag there and it will move without moving the text box.

If you want to get rid of the label and not use it, you can click to select it then just press the delete key.

If you want to keep it but not have it attached to the textbox any more, select the text box, and on the "Other" tab of the Properties Window, delete the name of the label next the "Label Name".

That did not work for me. After much digging I found out that Access 365 had a glitch that would not separate the two. I had to select all the field names and cut and then repaste on the form design. That make it work for me.

Usually if it keeps the label attached to the field it probably has layout applied. With layouts enabled, access will generally assign any unattached label to a nearby control that also doesn't have a label attached.