Background of the Sikh name `Singh'?

[Rajarshi Banerjee]

In most Indian languages and sanskrit singh or simha means lion.
The last name singh and sinha from UP, bihar are probably related.

My guess is that singh or sinha symbolizes a lion and the name is used to
denote a warrior caste. Early sikhs may have adopted names from those of
warrior classes of that period. Many rajputs and thakurs may have adopted
sikhism.

I would like to hear from someone who actually knows the history behind the
name.