I have the same issue. This is a desperately needed feature.
I submitted it as part of a larger scale Feature requests here: Make Emailing Better in Monday.com. Please vote. 
Interim Solution: Email Template Naming Convention
Because our email templates contain dynamic values, it’s critical to know which board is being used when sending them. We’ve encountered several issues where emails were sent from the wrong board, leading to significant errors.
To prevent this, I’ve implemented a naming convention to make it immediately clear which board each template is intended for.
Structure:
Each email template name follows this format:
[Board Code]-[Year (if relevant)]-[Program/Project Abbreviation]-[Key Details (if needed)]
Examples of Board Codes:
CON= Contacts boardORG= Organizations boardGA= Grant Applications board- (etc.)
If the year is relevant to the template, it comes next. Then, I include a short abbreviation/name for the project or program, followed by any specific details that clarify the email’s purpose. Additional important notes can be added at the end, if necessary.
Even though the structure has multiple parts, I keep subject lines short and easy to read.
Example:
If we’re emailing formal schools in 2025 from the Organizations board to send parents a survey, the template name would be:
ORG-2025-Formal-Awards Survey
I hope this helps!