Are you composing in Plain Text as this would explain why you see the */

How do I know if it is plain text?

I have tried everything and the * on each side of my name and title are still there.

In a 'Write' message, do you see a 'Formatting Bar' ? If no, can you enable it or not? See first image below

If there is no 'Formatting Bar' and you cannot select it then it is likely you are using 'Plain Text'.

Close the 'Write' window.

Is account set up for html? Right click on mail account name in Folder pane and select 'Settings' select 'Composition & Addressing' for the account select: 'Compose messages in HTML format' see second image below click on OK

Confirm mail account is set up to use HTML.

I have all that set up like you said. I do not see the * , the other person does on the receiving end. How do I know if my mail account is set to use HTML?

You can't force others to see your messages as you want them to be seen. You may be composing in HTML and seeing Bold but someone who views email in plain text mode will get alternatives; *Bold* is a common way of expressing bold text. Other possibilities are _underlined_ for underlined and /italic/ for italic.

The bad news is that you can't control what others see, nor how they choose to view their email.

I can't check this now, but there is an add-on (Signature Switch) which lets you select signatures on the fly. One capability is that its signature files can contain both plain text and "fancy" signatures and it will insert either one according to the mode chosen while composing. That in itself wouldn't help you, but if you send a message using both plain text and html, (Options|Delivery Format|Plain and Rich (HTML) text) then I am wondering if it will insert both signature variants as appropriate. If that all works, then your correspondents using plain text would see a plain text version of your signature which had no formatting markup.