Learn English – What’s the difference between a figure, a number and a digit

English does not have a word referring to this range specifically. Different languages divide up the world differently - this is one of those cases where the languages don't have equivalent terms.

The word teen or teens is close, but it has two limitations:

1. "Teen" refers only to 13 - 19; it cannot refer to 11 or 12. Recently, the term "tween" has been coined to refer to the ages 10-12 for this very reason.
2. "Teen" is most often found in reference to abstract ranges such as ages, years, temperatures and the like. So while we might refer to a "temperature in the teens" to mean a temperature between 13 - 19 (C or F), it's less common to refer to use it with concrete objects. It would be unusual or even wrong to say "I have teens of apples".

Since there is no specific term, you should instead use constructions such as:

• Eleven to nineteen
• In the low two digits
• About 15, 15 or so, around 15, 15 give or take...
• More than ten but less than twenty
• Ten-something (I think this is more understandable and common than the alternative 'tensomething')
• There is a slang term that is close to the meaning and usage, but its use may be marked in certain contexts and it is informal: umpteen; "It'll cost umpteen thousand dollars."
• Or finally, reword your statement to avoid the situation

You could say, "Pick a number from one to ten". This is usually understood to be inclusive - going from A to Z doesn't mean you start at B and end at Y, and working from Monday to Friday doesn't mean working only three days a week. Or, if you want to be extremely precise, say "Pick a number from one to ten, inclusive".