I converted the type size from points to inches and it's not true to size.

Sieablu,

How about this?

1) Tick Edit>Preferences>General>Use Preview Bounds;

2) Select the Type with the (normal) Selection Tool and Effect>Path>Outline Object;

3) Set the size as desired.

That will reduce the Bounding Box to the actual bounds of the letters, and keep the Type editable, so you can set the actual height of the (highest) letters.

If you need it as non outlined text in PDF (or maybe for other reasons), remove the effect:

4) With the live Type selected, in the Appearance palette click the Reduce to Basic Appearance button.

That will bring it back to normal plain Type, with no change in actual letter height.

Obviously, you will need to untick Use Preview Bounds for other purposes, but you can just tick that again when you need to edit (some of) the Type if needed to keep it in place; that may not be necessary because the changes will (mostly, and only if no letters exceed the hitherto vertical bounds) be in the horizontal direction.

You can't really apply a unit of linear measure to type-height that way. If that was my project, I'd just type a character, scale it to 2 inches tall, and note the size in points; then just set all the names at that size, in that font.

You''d have to decide which kind of character to key on. For instance, if you base it on uppercase O, which is often one of the tallest characters in a font, all your other characters will be under 2" tall, whereas if you base it on something less round, say, uppercase E, some of your characters will exceed 2".