XSLT 1.0 Capitalise each letter after non-alphanumeric character

For an XSLT 1.0 solution, you could setup a recursive template call that walks over each of the characters and tracks whether or not it has seen a alpha-numeric value, capitalizing the first that it sees, and then resetting when it encounters a non-alpha-numeric value:

<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns="http://www.w3.org/1999/xhtml">
  
  <xsl:variable name='text' select='"dInEsh sAchdeV kApil Muk"' />
  <xsl:variable name='lowers' select='"abcdefghijklmnopqrstuvwxyz"' />
  <xsl:variable name='uppers' select='"ABCDEFGHIJKLMNOPQRSTUVWXYZ"' />
  <xsl:variable name='numeric' select='0123456789'/>
  <xsl:variable name='alpha-numeric' select="concat($lowers,$uppers,$numeric)"/>
  <xsl:template match="/">
    
    <xsl:call-template name="capitalize">
      <xsl:with-param name="val" select="$text"/>
    </xsl:call-template>
    
  </xsl:template>
  
  <xsl:template name="capitalize">
    <xsl:param name="val"/>
    <xsl:param name="alphanumeric-seen" select="false()" />
    
    <xsl:variable name="head" select="substring($val, 1, 1)"/>
    
    <xsl:if test="$head">
      <xsl:variable name="is-alpha-numeric" select="not(translate($head, $alpha-numeric, ''))"/>
      <xsl:variable name="tail" select="substring($val, 2)"/>
      <xsl:choose>
        <xsl:when test="$is-alpha-numeric">
          <xsl:choose>
            <xsl:when test="$alphanumeric-seen">
              <xsl:value-of select="translate($head, $uppers, $lowers)"/>
            </xsl:when>
            <xsl:otherwise>
              <xsl:value-of select="translate($head, $lowers, $uppers)"/>
            </xsl:otherwise>
          </xsl:choose>
          <xsl:call-template name="capitalize">
            <xsl:with-param name="val" select="$tail"/>
            <xsl:with-param name="alphanumeric-seen" select="true()"/>
          </xsl:call-template>
        </xsl:when>
        <xsl:otherwise>
          <xsl:value-of select="$head"/>
          <xsl:call-template name="capitalize">
            <xsl:with-param name="val" select="$tail"/>
            <xsl:with-param name="alphanumeric-seen" select="false()"/>
          </xsl:call-template>
        </xsl:otherwise>
      </xsl:choose> 
    </xsl:if>
  </xsl:template>
  
</xsl:stylesheet>

With XSLT 2.0 you could use xsl:analyze-string and regex:

<xsl:stylesheet exclude-result-prefixes="#all" version="2.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns="http://www.w3.org/1999/xhtml">

  <xsl:variable name='text' select='"dInEsh sAchdeV kApil Muk"' />
  <xsl:variable name='lowers' select='"abcdefghijklmnopqrstuvwxyz"' />
  <xsl:variable name='uppers' select='"ABCDEFGHIJKLMNOPQRSTUVWXYZ"' />
  
  <xsl:template match="/">
   
    <xsl:analyze-string select="$text" regex="[a-zA-Z0-9]+">
      <xsl:matching-substring>
        <xsl:value-of select="upper-case(substring(., 1, 1)), lower-case(substring(., 2))" separator=""/>            
      </xsl:matching-substring>
      <xsl:non-matching-substring>
        <xsl:value-of select="."/>
      </xsl:non-matching-substring>
    </xsl:analyze-string>  
   
  </xsl:template>

</xsl:stylesheet>

I would also use a recursive named template - but instead of going over each character in text I would iterate on delimiters only:

XSLT 1.0 + EXSLT str:split() extension function

<xsl:stylesheet version="1.0" 
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:str="http://exslt.org/strings"
extension-element-prefixes="str">
<xsl:output method="xml" version="1.0" encoding="UTF-8" indent="yes"/>
<xsl:strip-space elements="*"/>

<xsl:param name="text">dInEsh sAchdeV kApil. muk O'connel derrick, Adrian-merriel james</xsl:param>

<xsl:variable name="lower" select="'abcdefghijklmnopqrstuvwxyz'" />
<xsl:variable name="upper" select="'ABCDEFGHIJKLMNOPQRSTUVWXYZ'" />

<xsl:variable name="punc" select="translate($text, concat($lower, upper), '')" />

<xsl:template match="/">
    <output>
        <xsl:call-template name="capitalize">
            <xsl:with-param name="text" select="translate($text, $upper, $lower)"/>
            <xsl:with-param name="delimiters" select="translate($text, concat($lower, $upper), '')"/>
        </xsl:call-template>
    </output>
</xsl:template>
    
<xsl:template name="capitalize">
    <xsl:param name="text"/>
    <xsl:param name="delimiters"/>
    <xsl:choose>
        <xsl:when test="$delimiters">
            <xsl:variable name="delimiter" select="substring($delimiters, 1, 1)"/>
            <xsl:call-template name="capitalize">
                <xsl:with-param name="text">
                    <xsl:for-each select="str:split($text, $delimiter)">
                        <xsl:value-of select="translate(substring(., 1, 1), $lower, $upper)"/>
                        <xsl:value-of select="substring(., 2)"/>
                        <xsl:if test="position()!=last()">
                            <xsl:value-of select="$delimiter"/>
                        </xsl:if>
                    </xsl:for-each>
                </xsl:with-param>
                <xsl:with-param name="delimiters" select="translate($delimiters, $delimiter, '')"/>
            </xsl:call-template>
        </xsl:when>
        <xsl:otherwise>
            <xsl:value-of select="translate(substring($text, 1, 1), $lower, $upper)"/>
            <xsl:value-of select="substring($text, 2)"/>
        </xsl:otherwise>
    </xsl:choose>
</xsl:template>

</xsl:stylesheet>

Result

<?xml version="1.0" encoding="UTF-8"?>
<output>Dinesh Sachdev Kapil. Muk O'Connel Derrick, Adrian-Merriel James</output>

However, this is not perfect: a sequence of consecutive delimiter character of the same kind will be reduced to a single character - e.g. alpha---bravo ==> Alpha-Bravo.